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Inve3000 MCQ Test Bank-2

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min xuan lim
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tions, Futures, and Other Derivatives, Ninth Edition Chapter 10: Mechanics of Options Markets “Multiple Choice Test Bank: Questions with Answers 1. Which ofthe following describes a call option? ‘A. The right to buy an asset for a certain price B. The obligation to buy an asset for a certain price C. The right to sell an asset for a certain price D. The obligation to sell an asset for a certain price Answer: A ‘Aca option isthe right, but not the obligation to buy. 2. Which of the following is true? ‘A. Along calls the same as a short put B. Ashort calls the same asa long put C Acall on a stock plus a stock is the same as a put D._ None of the above Answer: D None of the statements are true. Long calls, short calls, long puts, and short puts ll have different payoffs as indicated by Figure 10.5. 4 explained in Chapters 11 and 12 3. Aninvestor has exchange-traded put options to sell 100 shares for $20. There is a2 for 1 stock split. Which ofthe following Is the position ofthe investor after the stock split? ‘A. Put options to sell 100 shares for $20, B. Put options to sell 100 shares for $10 C._Put options to sell 200 shares for $10, . Put options to sell 200 shares for $20 Answer: € ‘When there isa stock split the number of shares increases and the strike price decreases. In this case, because itis a2 for 1 stock split, the number of shares doubles and the strike price halves. 4. An investor has exchange-traded put options to sell 100 shares for $20. There is 25% stock dividend. Which of the fllowing is the position ofthe investor after the stock dividend? ‘A. Put options to sell 100 shares for $20, B. Put options to sell 75 shares for $25 C. Put options to sell 125 shares for $15, D._ Put options to sell 125 shares for $16 Answer: D “The stack dividend Is equivalent toa 5 for 4 stock split. The number of shares goes up by 2504 and the strike price ls reduced to 4f5 ofits previous value, 5. An investorhas exchange-traded put options to sell 100 shares for $20, There isa $1 cash from the option premium. In the case of a very high stock price all options are exercised. The net payoff is zero and the gain is the same. 7. Which of the following is correct? A. Acalendar spread can be created by buying a call and selling a put when the strike prices are the same and the times to maturity are different B. Acalendar spread can be created by buying a put and selling a call ‘when the strike prices are the same and the times to maturity are different C. A calendar spread can be created by buying a call and selling a call when the strike prices are different and the times to maturity are different D. A calendar spread can be created by buying a call and selling a call when the strike prices are the same and the times to maturity are different Answer: D A calendar spread is created by buying an option with one maturity and selling an option with another maturity when the strike prices are the same and the option types (calls or puts) are the same. 8. What is a description of the trading strategy where an investor sells a 3-month calll option and buys a one-year call option, where both options have a strike price of $100 and the underlying stock price is $75? ‘A. Neutral Calendar Spread B. Bullish Calendar Spread C. Bearish Calendar Spread B. None of the above Answer: B This is a bullish calendar spread because a big increase in the stock price between three months and one year is necessary for the trading strategy to be profitable. fi, Which of the following is correct? ‘A. A diagonal spread can be created by buying a call and selling a put when the strike prices are the same and the times to maturity are different B. A diagonal spread can be created by buying a put and selling a call when the strike prices are the same and the times to maturity are different C. A diagonal spread can be created by buying a call and selling a call when the strike prices are different and the times to maturity are different D. A diagonal spread can be created by buying a call and selling a call when the strike prices are the same and the times to maturity are different Answer: C spread. Both the strike prices and times to maturity are different in a diagonal 10.Which of the following is true of a box spread? ‘A. It is a package consisting of a bull spread and a bear spread B. It involves two call options and two put options C. Ithas @ known value at maturity D. All of the above Answer: D A,B, and C are all true, 11.How can a straddle be created? ‘A. Buy one call and one put with the same strike price and same expiration date B. Buy one call and one put with different strike prices and same expiration date . Buy one call and two puts with the same strike price and expiration date D. Buy two calls and one put with the same strike price and expiration date Answer: A A straddle consists of one call and one put where the strike price and time to maturity are the same, It has a V-shaped payoff. 12.How can a strip trading strategy be created? ‘A. Buy one call and one put with the same strike price and same expiration date B. Buy one call and one put with different strike prices and same expiration date . Buy one call and two puts with the same strike price and expiration date D. Buy two calls and one put with the same strike price and expiration date Answer: C A strip consists of one call and two puts with the same strike price and time to maturity, 13.How can a strap trading strategy be created? ‘A. Buy one call and one put with the same strike price and same expiration date B. Buy one call and one put with different strike prices and same expiration date . Buy one call and two puts with the same strike price and expiration date D. Buy two calls and one put with the same strike price and expiration date Answer: D A strap consists of two calls and one put with the same strike price and time to maturity, 14,How can a strangle trading strategy be created? ‘A. Buy one call and one put with the same strike price and same expiration date B. Buy one call and one put with different strike prices and same expiration date . Buy one call and two puts with the same strike price and expiration date D. Buy two calls and one put with the same strike price and expiration date Answer: B A straddle consists of one call and one put where the times to maturity are the same but the call strike price is greater than the put strike price. 15.Which of the following describes a protective put? ‘A. Along put option on a stock plus a long position in the stock B. A long put option on a stock plus a short position in the stock CC. A short put option on a stock plus a short call option on the stock D. Ashort put option on a stock plus a long position in the stock Answer: A. A protective put consists of a long put plus the stock. The holder of the put ‘owns the stock that might become deliverable. 16.Which of the following describes a covered call? ‘A. Along call option on a stock plus a long position in the stock B. A long call option on a stock plus a short put option on the stock C. Ashort call option on a stock plus a short position in the stock D. A short call option on a stock plus a long position in the stock Answer: D A covered call consists of a short call plus a long position in the stock, The if the call is exercised the owner of the position has the stock ready to deliver if the other side exercises the call 17.When the interest rate is 5% per annum with continuous compounding, which of the following creates a principal protected note worth $1000? ‘A. A one-year zero-coupon bond plus a one-year call option worth about Sofi B. A one-year zero-coupon bond plus a one-year call option worth about Safi C. Aone-year zero-coupon bond plus a one-year call option worth about s3fi D. A one-year zero-coupon bond plus a one-year call option worth about s2fi Answer: B A one-year zero-coupon bond is worth 1000e%"*" or about $fi51. This leaves 1000-fi51 = $4fi for buying the option. 18.A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net gain (after the cost of the options is taken into account)? A. $100 B. $200 C. $300 D. $400 Answer: D The butterfly spread involves buying 100 options with strike prices $60 and $70 and selling 200 options with strike price $65. The maximum gain is when the stock price equals the middle strike price, $65. The payoffs, from the options are then, $500, 0, and 0, respectively. The total payoff is $500. The cost of setting up the butterfly spread is 11x100+18%100-14%200 = $100. The gain is 500-100 or $400. 1f.A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net loss (after the cost of the options is taken into account)? A. $100 B. $200 C. $300 D. $400 Answer: A The butterfly spread involves buying 100 options with strike prices $60 and $70 and selling 200 options with strike price $65. The maximum loss is when the stock price is less than $60 or greater than $70. The total payoff is then zero. The cost of setting up the butterfly spread is 11%100418x100-14%200 = $100. The loss is therefore $100. 20.Six-month call options with strike prices of $35 and $40 cost $6 and $4, respectively. What is the maximum gain when a bull spread is created by trading a total of 200 options? ‘A. $100 B. $200 c. $300 D. $400 Answer: © The bull spread involves buying 100 calls with strike $35 and selling 100 calls with strike price $40. The cost is 6x100—4x100=$200. The maximum payoff (when the stock price is greater than or equal to $40 is $500. The maximum gain is therefore 500 -200 = $300. Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 13: Binomial Trees Multiple Choice Test Bank: Questions with Answers 1, The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. Which of the following hedges the position? ‘A. Buy 0.6 shares for each call option sold B. Buy 0.4 shares for each call option sold . Short 0.6 shares for each call option sold D. Short 0.6 shares for each call option sold Answer: B ‘The value of the option will be either $4 or zero. If Ais the position in the stock we require 36—4=26A 4. it follows that 0.4 shares should be purchased for each so that A=! option sold, 2. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. What is the risk-neutral probability of that the stock price will be $36? A. 0. poe Answer: © The formula for the risk-neutral probability of an up movement is etd ud In this case w=36/30 or 1.2 and d=26/30 0.8667. Also 0 and 7-0.5. The formula gives p= P>(1-0.8667/(1 2-0.8667) “04. 3. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. What is the value of each call option? A. $1.6 B. $2.0 C324 D. $3.0 Answer: A ‘The formula for the risk-neutral probability of an up movement is pe ud In this case w-36/30 or 1.2 and d-26/30 -0.8667, Also gives and 7-0,5. The formula P=(1-0.8667/(1.2-0.8667) =0.4 ‘The payoff from the cail option is $4 if there is an up movement and $0 if there is a down movement, The value of the option is therefore 0144 =0.6*0 = S16. (We do not do any discounting because the interest rate is zero.) 4. The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. Which of the following is necessary to hedge the position? ‘A. Buy 0.2 shares for each option purchased B. Sell 0.2 shares for each option purchased C. Buy 0.8 shares for each option purchased D. Sell 0.8 shares for each option purchased Answer: © ‘The payoff from the put option is zero if there is an up movement and 4 if there is a down movement. Suppose that the investor buys one put option and buys A shares. if there is an up movement the value of the portfolio is x42. If there is a down movement it is worth 4x37+4, These are equal When 374+4=42A or A=0.8. The investor should therefore buy 0.8 shares for each option purchased. 5. The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. What is the value of each option? The risk-free interest rate is 2% per annum with continuous compounding A. $3.93 B. $2.93 c $193 D. $0.93 Answer: D ‘The formula for the risk-neutral probability of an up movement is Tad und In this case r=0.02, 7= 1, w=42/4 0.76 and the value of the option is (0.76%0+0.24% 4)«"*" 1.05 and d=37/40=0.925 so that 93 6. Which of the following describes how American options can be valued using @ binomial tree? ‘A. Check whether early exercise is optimal at all nodes where the option is in-the-money B. Check whether early exercise is optimal at the final nodes C. Check whether early exercise is optimal at the penultimate nodes and the final nodes D. None of the above Answer: A For an American option we must check whether exercising is better than not exercising at each node where the option is in the money. (It is clearly not worth exercising when the option is out of the money) 7. Ina binomial tree created to value an option on a stock, the expected return on stock is ‘A. Zero B. The return required by the market C. The risk-free rate D. Itis impossible to know without more information Answer: C ‘The expected retum on the stock on the tree is the risk-free rate. This is an application of risk-neutral valuation. 8. Ina binomial tree created to value an option on a stock, what is the expected return on the option? A. Zero B. The return required by the market C. The risk-free rate D. It is impossible to know without more information Answer: C The expected return on the option on the tree is the risk-free rate. This is an application of risk-neutral valuation. The expected return on all assets in a risk-neutral world is the risk-free rate. 9. Astock is expected to return 10% when the risk-free rate is 4%. What is the correct discount rate to use for the expected payoff on an option in the real world? A. 4% B. 10% C. More than 10% D. It could be more or less than 10% Answer: D The correct answer is D. There is no easy way of determining the correct discount rate for an option’s expected payoff in the real world. For a call option the correct discount rate in the real world is often quite high and for @ put option it is often quite low (even negative). The example in the text illustrates this. 10.Which of the following is true for a call option on a stock worth $50 ‘A. Asa stock's expected return increases the price of the option increases B. As a stock's expected retum increases the price of the option decreases C. Asa stock's expected return increases the price of the option might increase or decrease D. As a stock's expected return increases the price of the option on the stock stays the same Answer: D The option price when expressed in terms of the underlying stock price is independent of the return on the stock. To put this another way, everything relevant about the expected return is incorporated in the stock price. LL.Which of the following are NOT true A. Risk-neutral valuation and no-arbitrage arguments give the same option prices B. Risk-neutral valuation involves assuming that the expected return is the risk-free rate and then discounting expected payoffs at the risk- free rate C. Ahedge set up to value an option does not need to be changed D. All of the above Answer: C The hedge set up to value an option needs to be changed as time passes. A and B are true, 12.The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is the option price when u = 1.1 and d 0.9. A. $1.29 B. $1.49 c. $1.69 D. $1.89 Answer: 8 The probability of an up movement is = 0.6010 Pp The tree is = 3 43 Bo oss bs a Sa Lan 70 ass > oN Ss) 243 0 13.The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European put option on the stock with a strike price of $32 that expires in 6 months with u = 1.1 and d = 0.9. Each step is 3 months, the risk free rate is 8%. A. $2.24 B. $2.44 C. $2.64 D. $2.84 Answer: A. The probability of an up movement is = 0.6010 The tree is = 7 o a sar 228 —| 7s “ = 243 VW 114.Which of the following is NOT true in a risk-neutral world? The expected return on a call option is independent of its strike price B. Investors expect higher returns to compensate for higher risk C. The expected return on a stock is the risk-free rate D. The discount rate used for the expected payoff on an option is the risk- free rate > Answer: B In a risk-neutral world investors require an expected return equal to the risk-free rate and the discount rate that should be used for all expected payoffs is the risk-free rate 15.f the volatility of a non-dividend paying stock Is 20% per annum and a risk- free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter u for a tree with a three-month time step? A. 1.05 B. 1.07 C. 1.09 D111 Answer: D The formula for u is Los 16.1f the volatility of a non-dividend-paying stock is 20% per annum and a risk- free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter p for a tree with a three-month time step? A. 0.50 B. 0.54 c. 0.58 D. 0.62 Answer: 8 ‘The formula for p is ead _ et _ 0.9048 ee = 0.0048 9 538 u-d ~ 11052—0.9048 17.The current price of a non-dividend paying stock is $50. Use a two-step tree to value an American put option on the stock with a strike price of $48 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 20%. Which of the following is the option price? A. $1.95, B. $2.00 C. $2.05 D. $2.10 Answer: 8 In this case wee SF A1182 d= lw = 0.868 The tree is oun a8 S15855 oN az Se 199. 70 Ss a0 4558 Ss eee 10318 18.Which of the following describes delta? A. The ratio of the option price to the stock price B. The ratio of the stock price to the option price C. The ratio of a change in the option price to the corresponding change in the stock price D. The ratio of a change in the stock price to the corresponding change in the option price Answer: C Delta is a//As where AS is a small change in the stock price (with nothing else changing) and A/is the corresponding change in the option price. 19. When moving from valuing an option on a non-dividend paying stock to an ‘option on a currency which of the following is true? A. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate in all calculations B. The formula for u changes C. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate for discounting D. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate when p is calculated Answer: D The formula for u does not change. The discount rate does not change. The formula for p becomes showing that D is correct. 20.A tree is constructed to value an option on an index which is currently worth 100 and has a volatility of 25%. The index provides a dividend yield of 2% Another tree is constructed to value an option on a non-dividend-paying stock which is currently worth 100 and has a volatility of 25%. Which of the following are true? ‘A. The parameters p and u are the same for both trees B. The parameter p is the same for both trees but u is not C. The parameter U is the same for both trees but p is not D. None of the above Answer: C The formula for u is the same in the two cases so that the values of the index on its tree are the same as the values of the stock on its tree. However, in the formula for p, ris replaced by ~g Hull: Options, Futures and Other Derivatives, Ninth Edition Chapter 15: The Black-Scholes-Merton Model Multiple Choice Test Bank: Questions with Answers. 1. Which of the following is assumed by the Black-Scholes-Merton model? ‘A. The return from the stock ina short period of time is lognormal B. The stock price at 2 future time is lognormal C._The stock price at a future time is normal D. None of the above Answer: B Black-Scholes-Merton assumes that the return from a stock in a short period of time is ‘normally distributed. This means that the stock price ata future time is lagnormally distributed 2. The original Black-Scholes and Merton papers on stock option pricing were published in which year? A. 1983 8. 1984 c. 1974 D. 1973, Answer: D The correct answer is 1973. By coincidence this is also the year that organized trading in cal ‘options started. Put option trading started a few years later. 3. Which of the following isa definition of volatility ‘A. The standard deviation of the return, measured with continuous compounding, In one year 8. The variance of the return, measured with continuous compounding, in one year C. The standard deviation of the stock price in one year D. The variance of the stock price In one year Answer: A Volatility when multiplied by the square root of At isthe standard deviation of the retum in a short period of time of length At. Its also the standard deviation of the continuously ‘compounded return in one year. 4, Astock price is $100. Volatility is estimated to be 20% per year, What is an estimate of the standard deviation of the change in the stock price in one week? A. $0.38 8. $277 c. $3.02 D. $0.76 Answer: 8 The estimate is 1000.2 JT7S2 =82.77 5. What does N(x) denote? ‘A. The area under a normal distribution from zero tox B, The area under a normal distribution up to x © The area under a normal distribution beyond x D. The area under the normal distribution between -x and x Answer: 8 The normal distribution runs from minus infinity to plus infinity. N(x is the area under the distribution between minus infinity and x. 6. Which of the following is true for a one-year call option on a stock that pays dividends every three months? [A. tis never optimal to exercise the option early B. It canbe optimal to exercise the option at any time ._Itis only ever optimal to exercise the option immediately ater an ex-dividend date D. None of the above Answer: D When there are dividends itis sometimes optimal to exercise immediately before an ex: dividend date, but itis never optimal to exercise at other times. None of the first three answers are therefore correct. 7. What isthe number of trading days in a year usually assumed for equities? AL 365 8. 252 ©. 262 b. 272 Answer: B Analysts usually assume that there are 252 trading days ina year for equities. 8. The riskfree rate is 5% and the expected return on a non-dividend-paying stock is 12% Which of the following is a way of valuing a derivative? ‘A. Assume that the expected growth rate for the stock price Is 17% and discount the expected payoff at 12% 8B. Assuming that the expected growth rate for the stock price is % and discounting the expected payoff at 1236 (C_Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 5% D. Assuming that the expected growth rate forthe stock price is 12% and discounting the expected payoft at 5% Answer: Risk:neutral valuation shows that a derivative can be correctly valued by assuming that the stock grows a the risk free rate and discounting the expected payoff atthe risk-free rate. It follows that Cs the correct answer. 9. When there are two dividends on a stock, Black's approximation sets the value of an American call option equal to which of the following ‘A. Thevalue of a European option maturing just before the fst dividend B. The value of a European option maturing just before the secon¢ (final) dividend C The greater of the values in Aand 8 D. The greater of the value in 8 and the value assuming no early exercise Answer: D For Black’s approximation we calculate a) the value of the option assuming no early exercise ‘and b) the value ofthe option assuming that the exercise decision is made immediately before the final ex-dividend date. The value of the option fs set equal to the greater of these ‘two values. 410. Which ofthe following is measured by the VIX indox Implied volatilities for stock options trading on the CBOE B. Historical volatilities for stock options trading on CBOE C._ Implied volatilities for options trading on the S&P 500 index D._ Historical volatilities for options trading on the S&P SOO index Answer: ¢ ‘The Vix index measures the implied volatilities of one-month options trading on the S&P 500 index. 111, What was the original Black-Scholes-Merton model designed to value? ‘A European option on a stock providing no dividends B.A European or American option on a stock providing no dividends ‘CA European option on any stock . A European or American option on any stock Answer: ‘The original Black-Scholes-Merton madel was designed to value a European option on a stock paying no uhidends.. 12, A stock provides an expected return of 10% per year and has a volatility of 20% per year. What is the expected value of the continuously compounded return in one year? A. 6% B. 8% c. 10% D. 12% Answ ‘The expected value of the continuously compounded return per year is - 0° /2. In this case It is 0.1 ~0.2°R2 ff 0.08 or 8%, 13. An investor has earned 2%, 12% and -10% an equity investments in successive years (annually compounded). This is equivalent to earning which of the following annually compounded rates for the three year period. A. 133% B. 1.23% c. 1.13% D. 0.93% Answer: D Over the three year period $100 grows to 100x1.02x1.12x0.9 ff $102,816. This corresponds to an annually compounded return per year of 1.02816 ~ 1 =0.0093 or 0.93%. One plus the return Is the geometric average of 1.02, 1.12, and 0.90. 14, Which of the following is NOT true? ‘A Risk-neutral valuation provides prices that are only correct in a world where investors are risk-neutral B. Options can be valued based on the assumption that investors are risk neutral C. Inrisk-neutral valuation the expected return on all investment assets is set equal to the risk-free rate D. In risk-neutral valuation the risk-free rate Is used to discount expected cash flows Answer: A Risicneutral valuation produces a valuation that is correct in all situations not just those where investors are risk-neutral. The expected retum on all investments is assumed to be the riskfree rate and the risk-free rate Is used to discount expected payors, 15. Which of the following is a way of extending the Black Scholes-Merton formula to value 2 European call option on a stock paying a single dividend? ‘A. Reduce the maturity of the option so that it equals the time of the dividend B. Subtract the dividend from the stack price Add the dividend to the stock price D. Subtract the present value of the dividend from the stock price Answ To value a European option we replace the stock price by the stock price minus the present value of all dividends that have ex-dividend dates during the life ofthe option, 46. When the Black-Scholes-Merton and binomial tree models are used to value an option on anon- dividend. paying stock, which of the following Is true? ‘A. The binomial tree price converges to a price slightly above the Black-Scholes-Merton price as the number of time steps is increased B._ The binomial tree price converges to a price slightly below the Black-Scholes. Merton price as the number of time steps Is increased Either A or Ban be true DL The binomial tree price converges to the Black-Scholes-Merton price as the number of time steps is increased Answer: D ‘The binomial tree valuation method and the Black-Scholes-Merton formula are based on the same set of assumptions. As the number of time steps is increased the answer given by the binomial tree approach converges to the answer given by the Black-Scholes-Merton formula 417. When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following isthe price of a European call option on the stock A. 20N(0.1)-19.7N(0.2) B. 20N(0.2)-19-7N(0.1) C_19.7N(0.2)-20N(0.1) DL 18.7N(0-1}-20N(0.2) Answer: 8 ‘The formula for the option price is S.N(d,)- Ke™N(d,) In(S, / K) + (r-+.07 /2)7 ovr In this case So M120, r#0.06, off0.2, and 710.25 so that Ke’"f20e°**=f119,7. Also dd. ff [In(1)(0.06+0,04f2)0.25}fi(0.2x0.5) ff0.2 and d.ff0.2 ~0.2x0. 5#0.1. Bis therefore the correct answer. 4, and 18. When the non-dividend paying stock price i $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following isthe price of a European put option on the stock A. 19.7N(0.1)-20N(-0.2) 8. 20N(-0.1)-20N(-0.2), © 19.7N-0.2)-20N(-0.1), DL 20N(-0.2)-20N(-0.1) Answer: & ‘The formula for the option price is Ke" NGdy)= SNC) MS) /K)# (e402 /2)T and ds =F In this case 5, ff K #20, r 0.06, off0.2, and TAF0.25 so that Ke""f206°"°f19.7. Also «ff [In(2}+(0.06+0,042)0.25}4(0.2x0.5) 0.2 and u#40.2 ~ 0.20.54. Ais therefore the correct answer. 19. Asstock price is 20, 22, 19, 21, 24, and 24 on six successive Fridays. Which of the following is. Closest to the volatility per annum estimated from this data? A, 8 c D. Answer: D 50% 60% 7056 8036 ‘The price relative for the first week Is 22120 ar 1.1. The natural log of the price relative is |n(2.2) or 0.09533. similarly the in of the price relatives for the other weeks are -0.1466, 0.1001, 0.1335, and 0. The standard deviation of 0.09531, -0.1466, 0.1001, 0.1335, and 0 is 0.1138. The volatility per week is therefore 11.38%, This corresponds to a volatility per year of 0.1138 multiplied by the square root of 52 or about 82%. The answer is therefore D. 20. The volatility ofa stock is 18% per year. Which is closest to the volatility per month? AL 15% 8 3.0% C. 5.2% D. 6.3% Answer: € ‘The volatility per month is the volatility per year multiplied by the square root of 1f112 . The square root of 1ff12 Is 0.2887 and 18% multiplied by this is 5.2% Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 14: Wiener Processes and Ito’s Lemma Multiple Choice Test Bank: Questions with Answers 1. Avariable x starts at 10 and follows the generalized Wiener process dv=adi+h where time is measured in years. If « = 2 and » =3 what Is the expected value after 3 years? A. 12 B14 c. 16 D. 18 Answer: C The drift is 2 per year and so the expected increase over three years is 2x3 = 6 and the expected value at the end of 3 years is 10+6 = 16. 2. Avariable x starts at 10 and follows the generalized Wiener process dv=adt+h where time is measured in years. If u deviation of the value in 4 years? Aa 3.8 C12 D. 16 3 and b =4 what is the standard Answer: 8 The variance per year is 4? or 16. The variance over four years is 16x4 = 64. The standard deviation is /ea=8 3. Avariable x starts at 10 and follows the generalized Wiener process de=adi+h Bands What is the standard deviation of the value in three months? oners auNe Answer: B The variance per year is 42 or 16. The variance over three months is 160.25 = 4. The standard deviation is 3-2 4. The variance of a Wiener process in time t is At BL squared C. the square root of t D. tothe power of 4 Answer: A The variance of a Wiener process is 1 per unit time or «in time t 5. The process followed by a variable Vis GN mX desde ‘What is the coefficient of i in the process for the square of X. Dey ao © Dex nsx Answer: © From Ito's lemma, the coefficient of de is s'a//aX where f= A, Because af /ON =24, the coefficient of deis 201". 6. The process followed by a variable Wis dN = mX dttsNde ‘What is the coefficient of di in the process for the square of x eines = 2m? © mX2eN mXreX? Answer: A From Ito's lemma, the coefficient of ut is Lay OS sexe 2°" ax a {/X" =2the coefficient of deis 2mX+=!X* where f= 2%, Because af /av = Which of the following is true when the stock price follows geometric Brownian motion A. The future stock price has a normal distribution B. The future stock price has a lognormal distribution C. The future stock price has geometric distribution D. The future stock price has a truncated normal distribution Answer: B Ito's lemma show that the log of the stock price follows a generalized Wiener process. This means that the log of the stock price is normally distributed so that the stock price is lognormally distributed. 4. Ifa stack price fllaws e Markov process which ofthe fllowing could be true Whenever the stock price has gone up for four successive days it has a 70% chance of going up on the fifth day. B. Whenever the stock price has gone up for four successive days there is almost certain to be a correction on the fifth day. . The way the stock price moves on a day is unaffected by how it moved on the previous four days. D. Bad years for stock price retums are usually followed by good years. Answer: C A Markov process is a particular type of stachastic process where only the current value of a variable is relevant for predicting the future. Stock prices are usually assumed to follow Markov processes. This corresponds to a weak form market efficiency assumption, 9. Avariable x starts at zero and follows the generalized Wiener process, de~ade+ hile Where time is measured in years. During the first two years «=3 and )=4. During the following three years a=6 and h=3, What is the expected value of the variable at the end of 5 years A. 16 B. 20 . 24 D. 30 Answer: C During the first two years, the drift per year is 3 and so the total drift is 3x2 or 6. During the next three years, the drift per year is 6 and the total drift is 6x3 = 18. The total drift over the five years is 6+18 =24. Given that the variable starts at zero, its expected value at the end of the five years is therefore 24. 10. A variable x starts at zero and follows the generalized Wiener process dv adt= hile where time is measured in years. During the first two years @=3 and b=4. During the following three years «=6 and +=3. What the standard deviation of the value of the variable at the end of 5 years A. 6.2 5.67 ©. 72 D.77 Answer: D The variance per year for the first two years is 4” or 16. The variance per year for the next three years is 3 or 9. The total variance of the change over five years is 2x16+3x9= 59. The standard deviation of the value of the variable at the end of the five years is therefore {39 =7.7 JL. Ifa variable x follows the process dx = ds where d: is a Wiener process, which of the following is the process followed by y= exp(x’. f. dy=byde B dy = Osby devby de ©. dy = (v+0.5b'y) dry a D. dy= Osby divb de Answer: B Ito's lemma shows that the process followed by y is dy = 0.sh’exp(x) dt-+hexp(x de ‘Substituting y = exp(x) we get the answer in B. 12. Ifthe risk-free rate is and price of a nandividend paying stock grows at rate with volatility s, at what rate does a forward price of the stock grow for a forward contract maturing at a future time 7. 4m B. m—emi2 omar D. rst Answer: C This is the application of Ito's lemma in Section 14.6. 13. When a stock price, s, follows geometric Brownian motion with mean return ‘mand volatility » what is the process follows by where ¥ A. dX=mdr=s: BL N= nnn) di +s de C. dX = (m-s) dt +s a D. dy = (m= fi2) dt + de Answer: D This is the example in Section 14.7 14, Which of the following gives a random sample from a standard normal distribution in Excel? A. =NORMSINV() B. =NORMSINV(RAND()) C, =RND(NORMSINV()) RANDO Answer: B The correct instruction in Excel is =NORMSINV(RAND()) 15 Which of the following defines an Ito process? A. Aprocess where the drift is non-constant and can be stochastic B. A process where the coefficient of d: is non-constant and can be stochastic C. Aprocess where either the drift or the coefficient of d: or both are non- constant and can be stochastic D. Aprocess where proportional changes follow a generalized Wiener process Answer: C Ina generalized Wiener process the drift and coefficient of d= are both constant. In an Ito process they are not both constant 16, A stock price is $20. It has an expected return of 12% and a volatility of 25%. What is the standard deviation of the change in the price in one day. (For this question assume that there are 365 days in the year) $0.20 $0.23 $0.26 $0.29 goe> Answer: ‘The standard deviation of the change in one day is 200. 0.26 sx VI7305 17. Astock price is $20. It has an expected return of 12% and a volatility of 25%. What is the stock price that has a 2.5% chance of being exceeded in one day? (For this question assume that there are 365 days in the year.) A. $20.41 B. $20.51 c. $20.61 D. $20.71 Answer: B From the previous question the standard deviation of the change in one day is $0.26. There is a 2.5% chance that the stock price will increase by more than 1.96 standard deviations. The answer is therefore 20+1.96x0.26 = $20.51. The expected return in one day is small and can be ignored 8. Which of the following is NOT a property of a Wiener process? The change during a short period of time dr has a variance dt The changes in two different short periods of time are independent The mean change in any time period is zero The standard deviation over two consecutive time periods is the sum of the standard deviations over each of the periods oop> Answer D Variances of Wiener processes are additive but standard deviations are not, 19. If eis a random sample from a standard normal distribution, which of the following is the change in a Wiener process in time dt . A. etimes the square root of dt B. ctimes at C. urtimes the square root of « D. The square root of e times the square root of dt Answer: A, The change is eVa . This result is used when the process is simulated 20. For what value of the correlation between two Wiener processes is the sum of the processes also a Wiener process? A. 0.5 B. -0.5 co D1 Answer: B The variance of each process is 1 per unit time. The variance of the sum is 1+1+2p where p is the correlation. This is 1 when p=—0.5. Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 17: Options on Stock Indices and Currencies Multiple Choice Test Bank: Questions with Answers 1. Which of the following describes what a company should do to create a range forward contract in order to hedge foreign currency that will be received? ‘A. Buy a put and sell a call on the currency with the strike price of the put higher than that of the call B. Buy a put and sell a call on the currency with the strike price of the put lower than that of the call . Buy a call and sell a put on the currency with the strike price of the put higher than that of the call Buy a call and sell a put on the currency with the strike price of the put lower than that of the call v9 Answer: B The company wants to ensure that the price received for the foreign currency will be between & and >. It does this by buying a put option with strike price k; and selling a call option with strike price kz. 2. Which of the following describes what a company should do to create a range forward contract in order to hedge foreign currency that will be paid? ‘A. Buy a put and sell a call on the currency with the strike price of the put higher than that of the call B. Buy a put and sell a call on the currency with the strike price of the put lower than that of the call ©. Buy a call and sell a put on the currency with the strike price of the put higher than that of the call D. Buy a call and sell a put on the currency with the strike price of the put lower than that of the call Answer: D The company wants to ensure that the price paid for the foreign currency will be between Ki and &:. It does this by selling a put option with strike price &: and buying a calll option with strike price K: 3. What should the continuous dividend yield be replaced by when options on an exchange rate are valued using the formula for an option on a stock paying a continuous dividend yield? ‘A. The domestic risk-free rate B. The foreign risk-free rate C. The foreign risk-free rate minus the domestic risk-free rate D. None of the above Answer: B The continuous dividend yield, g, should be replaced by the foreign risk rate, r. 4, Suppose that the domestic risk free rate is r and dividend yield on an index is g. How should the put-call parity formula for options on a non-dividend-paying stock be changed to provide a put-call parity formula for options on a stock index? Assume the options last T years, ‘A. The stock price is replaced by the value of the index multiplied by exp(qT) B. The stock price is replaced by the value of the index multiplied by exp(rT) C. The stock price is replaced by the value of the index multiplied by exp(-qT) D. The stock price is replaced by the value of the index mult exp(rT) lied by Answer Sp is replaced by Sve™. 5. A portfolio manager in charge of a portfolio worth $10 million is concerned that stock prices might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What position is required if the portfolio. has a beta of 1? A. Short 200 contracts B. Long 200 contracts C. Short 100 contracts D. Long 100 contracts Answer: A The number of contracts required is 10,000,000/(500x100)=200. A short Position is required because the contracts must provide a positive payoff When the market declines. 6. A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What should the strike price of options on the index be the portfolio has a beta of 1? AL 425 B. 450 C. airs D. 500 Answer: C When the portfolio declines in value by 5%, the index can be expected to decline in value by 5%. The strike price should therefore be 0,95x500=4ff5. ff. A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What position is required if the portfolio has a beta of 0.57 A. Short 200 contracts B. Long 200 contracts . Short 100 contracts D. Long 100 contracts Answer: € ‘The number of contracts required is 0.5x10,000,000/(500%100)=100. A short position is required because the contracts must provide a positive payoff when the market declines 8. A portfolio manager in charge of a portfolio worth $10 million is concemed that the market might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $9.5 million. The index is currently standing at 500 and each contract is on 100 times the index. What should the strike price of options on the index be the portfolio has a beta of 0.57 Assume that the risk-free rate is 110% per annum and there are no dividends. ‘A. 400, B. 410 ©. 420 D. 425, Answer: D The risk-free rate per six months is 5%. When the portfolio declines by 5% its return is per six months is 10% below the risk-free rate. The return on. the index is therefore 20% below the risk-free rate. Its return is therefore 15%, The portfolio therefore declines to 500%0.85 = 425. 9. For a European put option on an index, the index level is 1,000, the strike Price is 1050, the time to maturity is six months, the risk-free rate is 4% per annum, and the dividend yield on the index is 2% per annum. How low can the option price be without there being an arbitrage opportunity? A, $50.00 B. $43.11 C. $29.21 D. $39.16 Answer: D A lower bound for the put option price is Ke~"-sw™. In this case, K=1050, 000, 7=0.5, r=0.04 and g=0.02. The lower bound is therefore 1050e e951 000e*°==39,16, The put price cannot fall below this without there being an arbitrage opportunity. 10.For a European call option on a currency, the exchange rate is 1.0000, the strike price is 0.9100, the time to maturity is one year, the domestic risk-free rate is 5% per annum, and the foreign risk-free rate is 3% per annum. How low. can the option price be without there being an arbitrage opportunity? A. 0.1048 B. 0.0900 c. 0.1344 D. 0.1211 Answer: A, A lower bound for the call option price is Se” — Ke? . In this case, K=0.9100, 50=1,0000, 1. 05 and -=0.03. The lower bound is therefore 1.00e°*-0,91¢2%"!=0,1048, The call price cannot fall below this without there being an arbitrage opportunity. 11.Index put options are used to provide protection against the value of the portfolio falling below a certain level. Which of the following is true as the beta of the portfolio increases? ‘A. The cost of hedging increases B. The required options have a higher strike price C. The number of options required increases D. All of the above Answer: D As beta increases A, B, and C are all true. 12.Which of the following is NOT true about a range forward contract? ‘A. Itensures that the exchange rate for a future transaction will lie between two values B. It can be structured so that it costs nothing to set up C. It requires a forward contract as well as two options D. It can be used to hedge either a future inflow or a future outflow of a foreign currency Answer: C A range forward contract requires two options only. A, B, and D are true. 13.4 binomial tree with three-month time steps is used to value a currency option. The domestic and foreign risk-free rates are 4% and 6% respectively. The volatility of the exchange rate is 12%. What is the probability of an up movement? ‘A. 0.4435 B. 0.526ff C. 0.5565 D. O.SfFfFL Answer: A. The parameter wis "M7 — 1.0618 and d= 1/u = 0.9418. The probability of an up movement is [e%°*-*%"°25—-9,9418]/[1.0618-0.9418] = 0.4435. 14.A binomial tree with one-month time steps is used to value an index option, The interest rate is 3% per annum and the dividend yield is 1% per annum The volatility of the index is 16%. What is the probability of an up movement? A. 0.4ff04 B. 0.5065 c. 0.5592 D. 0.5833 Answer: 8 The parameter wis cM" ~1.9473 and d= 1/u = 0.9549. The probability of an up movement is [e°°-"%"""_9.9418]/[1.04ff3—0.9549] = 0.5065. 15.A European at-the-money call option on a currency has four years until maturity, The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. ‘What is the value of the option? A, 0.98N(0.25)-1.11(0.05) B. 0.98N(-0.3)-1.11N(-0.5) C. 0.98N(.0.5)-1.11N(.0.ff) D. 0.98N(0.10)-1.11N(0.06) Answer: C The formula is c= Se 7 Nd, Ke™N(d,) IS, 1K) (rr, +o MT d, ovr d,=d,—oVT In this case S,e" =1.2e°"™ = 0.9825 and Ke’? =1 tn) + (0.02 0.05 +0.1°/2)4 Oe The correct answe we" 11077 4 d.=d,-0F =-07 therefore C. 16.A European at-the-money put option on a currency has four years until ‘maturity, The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. What is the value of the option? A. L.11N(0-ff)-0.98N(0.5) B. 1.11N(-0.f1)-0.98N(-0.5) C. LLIN(O.FF)-0.98N(0.4) D. 1.11N(-0.06)-0.98N(-0.10) Answer: A, The formula is p= Ke" NCd.)-Se 4 In(S,/K)+ rr, +0" 2 dy =d,-oT In this case S,e” =1.2e = 0.9825 and Ke"? =1.26“**=1.1077 _Ingl) + (0.020.054 0.1" /2)4 ove The correct answer is therefore A. 4, os dynd\-aVF =-07 1ff. Which of the following is true when a European currency option is valued using forward exchange rates? A. Itis not necessary to know the domestic interest rate or the spot exchange rate It is not necessary to know either the foreign or domestic interest rate It is necessary to know the difference between the foreign and domestic interest rates but not the rates themselves D. It is not necessary to know the foreign interest rate or the spot exchange rate oe Answer: D ‘The forward exchange rate contains all the information necessary about the foreign risk-free interest rate and the spot exchange rate. It is still necessary to know the domestic risk-free interest rate 18.What is the size of one option contract on the S&P 500? ‘A. 250 times the index B, 100 times the index C. 50 times the index D. 25 times the index Answer: B ‘One option is on 100 times the index 19.The domestic risk-free rate is 3%. The foreign risk-free rate is 5%. What is the k-neutral growth rate of the exchange rate? A. 42% B. 2% Cc. +5% D. 43% Answer: 8 The growth rate is 3% minus 5% or -2%. 20.What is the same as 100 call options to buy one unit of currency A with currency B at a strike price of 1.25? A. 100 call options to buy one unit of currency B with currency A at a strike price of 0.8 B. 125 call options to buy one unit of currency B with currency A at a strike price of 0.8 . 100 put options to sell one unit of currency B for currency A at a strike Price of 0.8 D. 125 put options to sell one unit of currency B for currency Aat a strike price of 0.8 Answer: D Buying 100 units of A with 125 units of B is the same a selling 125 units of B for 100 units of A Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 19: The Greek Letters ‘Multiple Choice Test Bank: Questions with Answers. 1. Acall option on a stock has a delta of 0.3. A trader has sold 1,000 options. What position should the trader take to hedge the position? ‘A, Sell 300 shares B. Buy 300 shares, . Sell 700 shares D. Buy 700 shares Answer: B When the stock price increases by a small amount, the option price increases by 30% of this ‘amount. The trader therefore has @ hedged position if he or she buys 300 shares. For small changes the gain or oss on the stack position is equal and opposite to the loss or gain on the option position. 2. What does theta measure? ‘A. The rate of change of delta with the asset price B._ The rate of change of the portfolio value with the passage of time C._ The sensitivity of a portfolio value to interest rate changes D. None of the above Answer: 8 Theta measures the rate of change In the value of a portfolio with the passage of time. 3. What does gamma measure? ‘A. The rate of change of delta with the asset price B, The rate of change of the portfolio value with the passage of time The sensitivity of a portfolio value to interest rate changes D. None of the above Answer: A Gamma measure the rate of change of delta with the asset price. 4. What does vega measure? ‘A. The rate of change of delta with the asset price 8. The rate of change of the portfolio value with the passage of time C_The sensitivity of a portfolio value to interest rate changes D. None of the above Answer: D \Vega measures the rate of change of the value of the portfolio value with volatility. What does rho measure? A. The rate of change of delta with the asset price B._ The rate of change of the portfolio value with the passage of time C. The sensitivity of a portfolio value to interest rate changes D._ None of the above Answer: © Rho measures the rate of change of the value of the portfolio with interest rates. (Usually a parallel shift in interest rates is considered.) Which of the following is true? A. The delta ofa European put equals minus the delta of a European call B. The delta of a European put equals the delta of a European call CC. The gamma of a European put equals minus the gamma of a European call ._ The gamma of a European put equals the gamma of a European call Answer: D The delta of a put on a non-dividend-paying stock equals the delta of the call minus one. The gamma of a put equals the gamma of call even when there are dividends. {A portfolio of derivatives on a stock has a delta of 2400 and a gamma of -10. An option on the stock with a delta of 0.5 and a gamma of 0.04 can be traded. What position in the option is necessary to make the portfolio gamma neutral? ‘A. Long position in 250 options B. Short position in 250 options Long position in 20 options 1. Short position in 20 options Answer: A ‘The options must have @ gamma of 1110 to neutralize the gamma of the portfolio. Each option hhas a gamma of 0.04. Hence a long position of 10/0.04 = 250 options is required. A trader uses a stop-oss strategy to hedge a short position in a three-month call option with a strike price of 0.7000 on an exchange rate. The current exchange rate is 0.6950 and value of the option is 0.1. The trader covers the option when the exchange rate reaches 0.7005 and uncovers {e, assumes 2 naked position) i the exchange rate falls to 0.6995. Which of the following is NOT true? ‘A. The exchange rate trading might cost nothing so that the trader gains 0.1 for each option sold The exchange rate trading might cost considerably mare than 0.1 for each option sold so that the trader loses money The present value of the gain or lass from the exchange rate trading should be about 0.1 con average for each option sold D._ The hedge works reasonably well Answer: D A good hedging system will ensure that the cost of selling an option is close to its theoretical value. The stop-loss hedging procedure does not have this property. It can lead to the option ‘costing nothing or costing considerably more than its theoretical value. On average the cost of the option ists Black-Scholes value, but there isa wide variation. D isthe correct answer, 9. Maintaining a delta-neutral portfolio is an example of which of the following ‘A. Stop-loss strategy 8. Dynamic hedging C. Hedge and forget strategy D. Static hedging Answer: B Delta-neutral hedging is an example of dynamic hedging. The hedge has to be adjusted periodically, (In theory, to maintain a delta-neutral hedge, the hedge must be adjusted continuously.) 10. Which of the following could NOT be a delta-neutral portfolio? ‘A. Along position incall options plus a short position in the underlying stock B.A short position in call options plus a short position in the underlying stock . Along position in put options and a long position in the underlying stock 1. Along position in a put option and a long position in a call option Answer: 8 Calls have a positive delta. Puts have a negative delta. A long stock position has a positive delta {A short stock position has @ negative delta. 8 cannot be delta neutral (ie., have a delta of zero) because both parts of the portfolio have a negative delta 111. Which of the following is NOT true about gamma? A. A highly positive or highly negative value of gamma indicates that a portfolio needs frequent rebalancing to stay delta neutral 5, The magnitude of gamma is a measure of the curvature of the portfolio value as a function of the underlying asset price .Abig positive value for gamma indicates that a big movement in the asset price in either direction will lead to a loss D. Along position in either a call or a put has a positive gamma Answer: C Cis not true. The change in the value is a gain of O.SP'AS’. There isa gain from a big movement when gamma is positive and a loss from a big movernent when gamma is negative, 12. Gamma tends to be high for which of the following A. At-the money options 2. Outof-the money options C._In-the-money options . Options with a long time to maturity Answer: A Gamma tends to be high for at-the-money options. See Figure 19.9. 13. Which of the following is true for 3 call option on a non-dividend-paying stock when the stock’s price equals the strike price? A. Ithasa delta of 0.5 8. thas adelta ess than 0.S CC. Ithas a delta greater than 0.5 D. Delta can be greater than or less than 0.5 Answer: C ‘The delta is Nd) where HIM. K) (r+ 0" 27 oT From this it can be seen that, when (eso" (2WF This Is always positive. Hence delta Is always greater than 05. Kyhis 14, The riskefree rate i $% and the dividend yield on an index is 2%. Which of the following is the delta with respect to the index for a one-year futures on the index? A. 0.98 8. 1.05 c. 1.03 D. 1.02 Answer: C The futures price is given by Hence the delta of the futures with respect to the spot is e" ot 03 415, The gamma of a delta-neutral portfolio is $00. What Is the impact of a jump of $3 in the price of the underlying asset? A. Again of $2,250 B. Aloss of $2,250 C. Again of $750 D. Aloss of $750 "In this case, this is Answer: A The change in the value is a gain of 0.51'AS* = 0.5x500x3"=52,250. 16. Vega tends to be high for which of the following, ‘A. Atthe money options 8. Outof-the money options .In-the-money options D. Options with a short time to maturity Answer: A. \Vega tends to be high for at-the-money options. See Figure 19.11. 17. The delta of a call option on a non-dividend-paying stock is 0.4. What is the delta of the corresponding put option? A 04 8B. 04 c. -06 D068 Answer: C The delta of a call option is (cj) and the delta of a put is N(aj)-2. When (di 0.6. = 0.4, Nat)-Lis 18. A call option on a non-dividend-paying stock has a strike price of $30 and a time to maturity of sik months. The risk free rate Is 4% and the volatility Is 25%. The stock price is $28. What is the dalta of the option? A N(-0.1342) BL N(0.1888) Cc. N{-0.2034) D. Nt-0.2241) Answer: B The delta is Nu) where 4 =IMSLA) +40" 27 . ov? In this case In(28/30) + (0.04 + 0.257/2) x0.5 qe OE ER == OL 888) 025005 Which of the following is NOT a letter in the Greek alphabet? A. delta B. tho C vega ©. gamma Answer: € Vega, although itis referred to 2 "Greek letter” by option traders, is nota letter in the Greek alphabet. Which of the following is true for a long position in an option A. Both gamma and vega are negative B. Gamma is negative and vegas positive CC. Gamma is positive and vega is negative D. Both gamma and vega are positive Answer: D Gamma and vega are both positive for a long position in an option. It does not matter whether ‘the option is a call ora put.

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