Option Calculator
Price of the underlying 73.5000 11600.00 11700.00 11800.00 11900.00
Risk-free interest rate (%) 0.0 0.0 0.0 0.0 0.0
Strike price 74.5000 75 75 75 75
Annual volatility (%) 5.9 5.9 5.9 5.9 5.9
Time to expiration (days lef 30 30 30 30 30
Dividend yield (%) 0.0 0.0 0.0 0.0 0.0
Price of Call Option 0.15074 11525.50 11625.50 11725.50 11825.50
Price of Put Option 1.150740 0.00 0.00 0.00 0.00
Delta for Call Option 0.215 1.000 1.000 1.000 1.000
Delta for Put Option -0.785 0.000 0.000 0.000 0.000
Theta for Call Option -0.006 0.000 0.000 0.000 0.000
Theta for Put Option -0.006 0.000 0.000 0.000 0.000
Gamma for Call Option 0.235 0.000 0.000 0.000 0.000
Gamma for Put Option 0.235 0.000 0.000 0.000 0.000
Vega for Call Option 0.062 0.000 0.000 0.000 0.000
Vega for Put Option 0.062 0.000 0.000 0.000 0.000
Rho for Call Option 0.013 0.061 0.061 0.061 0.061
Rho for Put Option -0.048 0.000 0.000 0.000 0.000
Impact of Delta
Call Premium 175.11 Put Premi 175.11
Delta 0.507748 Delta -0.492252
Proof- Inc in spot price Call Premuim 175.62 Put Premuim 174.62
New Delta 0.508657 Change in 0.001
Impact of Volatility Call Premium 175.11 Put Premi 175.11
Vega 9.727128 Vega 9.727128
Proof Inc in 1% Vol Call Premuim 184.84 Put Premui 184.84
Inpact of Theta Call Premium 175.11 Put Premi 175.11
Theta -5.149656 Theta -5.149656
Call Premuim 169.96 Put Premui 169.96
Inpact of Rho Call Premium 175.11 Put Premi 175.11
Rho 2.590728 Rho -2.672286
Call Premuim 177.70 Put Premuim 172.44
Position Greeks= option Greeks x quantity
Delta
OTM ?
ATM ?
ITM ?
Shows the speed in the incerease in the premium of the options as option moves ITM
Important points for Delta
As the expiry comes closer delta of ATM moves closer to 0.5, OTM to 0 and ITM to 1
sum of Abs values of call and put deltas of same strike will always be 1
Every option has its unique delta as the inputs are different and hence it’s a dynamic number not static. You change the input t
Future has 1 delta
Buying calls means Long Delta, selling calls means short delta
Buying puts means short delta and selling puts means long delta
Volatility/ Vega
represents change in premium of option due to one percent change in volatility
Behaviour of Vega:
Spot 11000 11500 12000
11500 CE OTM ATM ITM
11500 PE ITM ATM OTM
CE=PE=VEGA Will have sa Will have Will have same impact
Spot 11000 11100 11200 11300 11400 11500 11600
VEGA 5.44045932 6.828287 8.106788 9.117624 9.72803 9.859921 9.506123
Impact of the Volatility change will be highest at?
Behaviour of Vega:
Longer the maturity the higher will be the VEGA and hence the impact of Volatiliy will be higher. At maturity Vega is almost zero
While delta impacts the intrinsic value, VEGA impacts the time value of the option
VEGA is always positive. It means increase is favourable to option_____and not favourale to option____?
Buy call or Buy puts means VEGA long or Long Volatlity and Sell Call and Sell put means Short Vega or short volatility
Future VEGA is always 0
Can a Future long plus Long put can be VEGA neutral?
THETA
represent the change in option premium due to change in time.
Behavior of Theta
Spot 11000 11100 11200 11300 11400 11500 11600
THETA of call -3.1393825 -3.982993 -4.79143 -5.477166 -5.963751 -6.202002 -6.179746
Theta highest at?
Theta is favourable for option___and unfavourable for option____
Both puts and calls have ______Theta
Buying calls and puts means theta negative and selling calls and puts means theta positive
Theta is at peak at ATM option and decreases as spot moves away from ATM
Behaviour of theta w.r.t Volatility
Higher the Volatility higher will be the premium of the option and hence higher will be the theta decay
Example Spot Srike Volatility Premium Days to expTheta Average d
Nifty 12000 12000 20% 209 15 -7.5 -13.9
Stock XYZ 12000 12000 40% 402 15 -14 -26.8
Theta w.r.t time to maturity
Theta is NOT average decay in the premium. As the maturity comes closer ATM theta decay tends to increase, it means the sp
Example Spot 15 DAYS 14 DAYS 13 DAYS 12 DAYS 11 DAYS 10 DAYS
Nifty spot 12000 -7.5 -7.7 -7.9 -8.2 -8.5 -8.9
Strike 12000
Volatility 20%
Int 6%
How the theta of OTM will behave w.r.t time?
Call Sell & Put Sell -Theta will be positive for the seller
Call Buy and Put Buy -Theta will be negative for the buyer
If our position theta is positive, to make it theta neutral we have to _____options (Buy or Sell)?
If our position theta is negative, to make it theta neutral we have to _____options (Buy or Sell)?
Excercises
1. open Option oractle and make a Bull spread to understand the combined effects of Delta, Vega and theta
2. Build an option strategy and understand the impact on expected returns if market inputs change.
Option strategies
1- Gamma short strategy
Gamma short itself means- Selling options- because gamma itself is a positive number so selling gamma means selling options
Sell one slight OTM put
Sell One OTM call based on the delta of the put to make it delta neutral
Buy one deep OTM call and put - weekly option to make the strategy delta neutral and hedged all the times to avoid any big Ga
Objective
The objective of the strategy is to earn only TV and it is direction neutral
Delta is our enemy as we are gamma short which means any change in delta is against us (any change up or down)- So we wa
Vega will give us gain if Volatility comes down as we are Vega short, But we will loose if Volatility goes up
Theta is positive and hence we will gain as time passes by
Adjustment Required
Delta range +/- 10 for 1 lot size is ok to handle, a reasonable price movement should be there to make it delta neutra
Switch the positions as delta changes and make it again delta neutral
Stop loss
Stop out one leg if the delta of any option leg approaches to more than 0.6 or the premium got more than double from your leve
Make the position again delta neutral based upon the delta of the other position left
How can we neutralise the delta
1. Buy future or stock
2. Buy options- this will have double benefit, hedge and delta netrual
Another Version of the strategy
Low Delta Short Gamma
We know far OTM has low delta
and short gamma means short options
So strategy is to sell far OTM options
With an uderstanding that theta decay of Far OTM will be higher in % terms
Lets See:
spot 11300
Call Price- 11300 286
Put Price - 11300 231
DTE 30
Time taken for premiu 22 days
For 11600 options 157
Time taken for premiu 15
for 11800 100
Time taken for premiu 12
Spot 11300
Int 0%
Strike 11300
Annual Vol 18%
Time to exp 17
r not static. You change the input the delta will change
Vega
12
11700 11800 11900 12000
8.729169 7.644033 6.391111 5.107896 10
6
Vega
12
10
8
her. At maturity Vega is almost zero
6
o option____?
hort Vega or short volatility 4
0
1 2 3 4 5 6 7 8 9 10 1
11700 11800 11900 12000 Theta
-5.922408 -5.484885 -4.937839 -4.352801
0
1 2 3 4 5 6 7 8 9 10 11
-1
-2
-3
-4
At expiry -5
0
0 Seller of the option -6
-7
y tends to increase, it means the speed of fall in premium due to reduction in time to maturity will increase. So a weekly option and a monthl
5 DAYS 2 DAYS 1 DAY
-12.2 -18.7 -26.0
Vega and theta
elling gamma means selling options
ed all the times to avoid any big Gap ups and downs
any change up or down)- So we want delta to be neutral always
atility goes up
uld be there to make it delta neutral
ot more than double from your level
8 9 10 11
10 11
eekly option and a monthly option will not see same fall due to time.
Cmp (S) 9106
Excersise price (E) 9000
Time (Days to Expiry in years) 0.0192
Volatility 20%
Rf 0.06
Exp 1 Exp 2 Exp 3
N(d1) 0.011708959576371 0.001534246575342 0.027696990588713
N (d2) 0.011708959576371 0.000767123287671 0.027696990588713
Exp 1 Exp 2 Value of call option
Theoratical Value of options 6226.02 6057.29 168.73
Actual Price in market 169
In a Call option It is the In a put option It is the In nutshell, this is a
probabilty that price will probabilty that price will probability the option
N (d1) = be above strike price . be lower than strike will be in the money
price .
It is the probabilty that In a put option It is the
the strike will be lower probabilty that strike
N (d2) = than spot price . will be higher than
strike price .
1.0396039604
(d1) N(d1) Probablity of upside
0.47814603212 0.683727 Delta of Call
-0.316273 Delta of a Put
0.45044904153 0.673807 Probablity of downside
-0.326193
Value of put
52.38 C= S x N(d1) – E x e-rtN(d2)
107
54.62 S + P = C + E x e-rt = Put - Call parity
9158.38 9158.38 1
Theoratical
8989.65
Actual 9213 9158.65 54.3502083
115.3659
40
Probablity of upside
Probablity of downside
all parity
S+P C+(E*e^-rt)
168.731 C= S+P-(E*e^-rt)
168.731
Cmp (S) 74.33
Excersise price (E) 74.5 Value of options? Both call and put
Time (Days to Expiry in years) 0.0822 No of days left in expiry - In years
Volatility 5% Implied Volatility
Rf (foreign) 0%
Rf (domestic) 8%
Exp 2: Effect on Exp 3: Effect of
returns due to Volatility for time (t)
Exp 1:- Log Returns of volatility and risk free
underlying over rate for tme t (Both
exercise price Sides)
N(d1) -0.002284486648312 -0.006491671103132 0.012936101624616
N (d2) -0.002284486648312 -0.006659013828375 0.012936101624616
Exp 1 Exp 2 Value of call option
Theoratical Value of options 18.37 18.23 0.1406
Actual Price in market
Calls Puts
In a Call option It is the In a put option It is the In nutshell, this is a
probabilty that Spot price probabilty that price will probability the option
N (d1) = will be above strike price
on the expiry.
be lower than strike
price .
will be in the money
It is the probabilty that In a put option It is the
the strike will be lower probabilty that strike will
than spot price . be higher than strike "The expression N(d2)
price . is the probability that
the option will be
N (d2) = excersied, so that
KN(d2) is the strike
times the probablity
that the strike price will
be paid"*
*John C Hull- Page no 292, Chapter 13
Black and Scholes Model
Norm.Dist- Which gives us the probabilty if we give mean and std dev
(d1 & d2) N(d1) & N(d2)-
Volatility Probality of
Adjusted the returns
returms
-0.6784236864 0.2487515475 Delta of Call
-0.7512484525 Delta of a Put
-0.691359788 0.2446697339
-0.7553302661
Value of put
0.31 C= S x N(d1) – E x e-rt X N(d2)
Discounted Exercise price
-0.31 S + P = C + E x e-rt = Put - Call parity
74.64 74.64 1
Theoratical
l- Page no 292, Chapter 13 74.5
Actual 74.33 74.5 -0.17
0.034982
40
all parity
S+P C+(E*e^-rt)
0.14063 C= S+P-(E*e^-rt)
0.14063
Black & Scholes Option Pricing Calculator
Price of the underlying 250.00 Strike price nearest to spot level 250
Risk-free rate of interest(%) 9.0 Strike price interval 10
Annual volatility (%) 20.0
Time to expiration (days left) 28
Dividend yield (%) 0.0
How to USE this calculator Strike Price Premium Delta Theta Gamma Vega Rho
Call option 220 31.55 0.993 -0.058 0.001 0.013 0.166
Put option 220 0.03 -0.007 -0.004 0.001 0.013 -0.001
Call option 230 21.87 0.951 -0.078 0.007 0.070 0.166
Put option 230 0.29 -0.049 -0.022 0.007 0.070 -0.010
Call option 240 13.11 0.813 -0.113 0.019 0.186 0.146
Put option 240 1.46 -0.187 -0.055 0.019 0.186 -0.037
Call option 250 6.41 0.561 -0.130 0.028 0.273 0.103
Put option 250 4.69 -0.439 -0.069 0.028 0.273 -0.088
Call option 260 2.44 0.289 -0.102 0.025 0.237 0.054
Put option 260 10.65 -0.711 -0.038 0.025 0.237 -0.144
Call option 270 0.70 0.108 -0.052 0.013 0.129 0.020
Put option 270 18.85 -0.892 0.014 0.013 0.129 -0.186
Call option 280 0.15 0.029 -0.018 0.005 0.046 0.005
Put option 280 28.23 -0.971 0.050 0.005 0.046 -0.208
