Currency Options

Currency Options
A currency option contract gives the buyer (or holder) the right,
but not the obligation, to buy or sell foreign currencies in future
Options can be over-the-counter (OTC) or exchange traded
OTC options are customized agreements hedge the risk
associated with a specific security
Exchange-traded options have greater liquidity.

2
5
 Basic Option Pay-Offs at Expiry
• At expiry, an American call option is worth the
same as a European option with the same
characteristics.
• If the call is in-the-money, it is worth ST – E.
• If the call is out-of-the-money, it is worthless.
• Call option value at expiry:
CaT = CeT = Max[ST - E, 0]

6
 Basic Option Profit Profiles(Long Call)

P = Max[Spot - E, 0]
profit

$/£ =1 .7500

ST

-P= 0.005 E

loss Maximum you pay is: 1.750+0.005 = 1.755

7
 Basic Option Profit Profiles(Short
Call)

profit
CaT = CeT = Max[ST - E, 0]
$/£ =1 .7500
Ca= 0.79
ST

loss

8
 Basic Option Profit Profiles(Long Put)

profit PaT = PeT = Max[E - ST, 0]

ST
E-p
E

loss

9
Basic Option Profit Profiles(Short
Put)
profit
CaT = CeT = Max[ST - E, 0]

ST
E-p E

loss

10
 Call Options Value
Profit

CaT > Max[ST - E, 0]

Market Value
Time value
Intrinsic value
ST
E
Out-of-the-money In-the-money
loss

11
 Hedging with Options
• An FX option contract gives the buyer the right, but not the
obligation, to:
– Buy Pound against US Dollars
• Consider the case of the importer who expects to pay £ 1
million in 6 months.
• The importer currently has three choices:
– Leave exposure open, and sales dollars spot to buy pound
– Cover exposure by selling dollars forward to buy pound
– Enter into a currency option to buy pound against dollars

12
Bloomberg Rs-USD Option Screen Shot

13
 European Call Option Pricing Formula
C = [ S e − rft N (d1 ) − Xe− rdt  N (d 2 )]
Where
C = the value of a European Call option at time t
rf = the interest rate in the U.S. & rd = the interest rate in India
r = the interest differential between India and the US
S= Spot rate & X= Exercise price

where, N(d) is the probability that a random draw from a standard normal distribution
will be less than d. This equals the area under the normal curve upto “d”.

1 2
ln( S / X ) + (r +  ) T d 2 = d1 −  T
d1 = 2
 T
14
 where, N(d) is the probability that a random draw from a standard
normal distribution will be less than d. This equals the area under
the normal curve upto d.
• If both N (d) terms are close to one, that is, when there is a very
high probability the option will be exercised, then the certainty
case.
• If N (d) terms are close to zero, meaning the option almost
certainly will not be exercised. Then, call is worth 0.
• For the values of N (d) between 0 and 1, the call value can be
viewed as the PV of the call’s potential payoff adjusting for the
probability of in-the-money expiration.
• Notice that, ln (S/X) is » the % amount by which the option is
currently in or out of the money. The spot adjusts the amount by
which the option is in or out of the money for the volatility of the
stock price over the remaining life of the option.
• An option in the money by a given % is more likely to stay in the
money if both exchange rate volatility and time to maturity are
small.
• N (d1) & N (d2) increase with the probability that the option will
expire in the money.
15
 Implied Volatility
Derived from Black-Scholes(1973) model

C = [S N (d ) − e−rT X N (d − t )]
where, N(d) is the cumulative distribution function of a standard normal calculated
at d

1 2
ln( S / X ) + (r +  ) T
d= 2
 T
• Implied volatility depended on the maturity of the option
• Implied volatility differs with the strike price of option
(creating volatility smiles or skews) so one can take derive
a measure of weighted average volatility
 Volatility Forecasting in GARCH
 2 t =  +  ut2−1 +  t2−1
 2
t = V +  u 2
t −1 +  2
t −1

 2
t = (1 −  −  ) V +  u 2
t −1 +  2
t −1

See Hull Page 226 for the solutions..

 2
t =V + ( +  ) (t 2
t −1 −V )
You only need the volatility today to forecast
tomorrow’s volatility, given the long run volatility
Sensitivity of Option Price to Change
in its Determinants
• Sensitivity to Changes in Spot FX Rate
– Referred to as Delta
– C/S
– Measured as the change in option value for a
change in spot currency value of 1% or 1 unit
• Sensitivity of Delta to change in Spot FX Rate
• Referred to as Gamma
• 2C/S2
• Captures the second order of risk

18
 Sensitivity of Option Price to Change
in its Determinants
• Sensitivity to Changes in Elapsed Time
– Referred to as Theta
– C/T
– Measured as change in option value for a one day reduction
in time to maturity (all other parameters remaining
constant)
• Sensitivity to Changes in Interest Rates
– Referred to as Rho
– C/r
– Measured as change in option value for a one basis point
increase in interest rates (all other parameters remaining
constant).

19
Sensitivity of Option Price to Change
in its Determinants
• Sensitivity to Changes in Implied Volatility
– Generally referred to as Vega or Kappa
– C/V
– Measured as change in option value for a
change in implied volatility of 1%

20
Sensitivity of Option Prices to Change in Factors
Delta = change in price of an option
Change in price of underlying bond
gamma= change in delta
Change in price of underlying bond
theta= change in price of an option
decrease in time to expiration
kappa= change in price of an option
1% change in expected volatility

21
 Currency Hedging with Options
• Consider the case of the importer who expects to pay
USD 10 million in 1 Year time.
• The importer currently has three choices:
– Leave exposure open, and buy USD spot
– Cover exposure by buying USD forward
– Buy a currency option for US dollars

22
 Hedging Alternatives
• Forward Market Hedge
• Money Market Hedge
• Options Market Hedge
• Cross-Hedging Minor Currency Exposure
• Hedging Contingent Exposure
• Hedging Recurrent Exposure with Swap Contracts
 Hedging Alternatives
• Consider the case of the importer who expects to pay £ 1 million in one-
year from now.
• The importer currently has the following choices:
– Leave exposure open, and sales Rupees spot to buy £ 1 million
• Undertakes Rs- £ exposure as open position
– Cover exposure by selling Rs forward to buy pound
• Fully hedged against £
– Cover exposure by selling dollars forward to buy pound, and buys $ spot
• Subject to Rupee-Dollar spot risk, speculates on Rs/ $
– Undertakes a money market operation, by borrowing Rupees,
converting into £, and investing for one-Year
– Enter into a currency option to buy £ against $ or Rupees against £
 Unhedged vs Forward vs Call Option

Unhedged

profit
Option
Rs/$=70.00
Forward
ST
E

loss Rs/$=70.00+1.00= 71.00

Thank You