Problem 7.15 U.S. Dollar/British Pound- How much more would a call option on pou
ID: 2814782 • Letter: P
Question
Problem 7.15 U.S. Dollar/British Pound- How much more would a call option on pounds be if the maturity was doubled from 90 to 180 days? What percentage increase is this for twice the length
of maturity?
Problem 7.15 U.S. Dollar/British Pound- How much more would a call option on pounds be if the maturity was doubled from 90 to 180 days? What percentage increase is this for twice the length
of maturity?
Pricing Currency Options on the British pound A U.S.-based firm wishing to buy A British firm wishing to buy or sell pounds (the foreign currency) or sell dollars (the foreign currency) Variable Value Variable Value Spot rate (domestic/foreign) S0 $1.87 S0 £0.5355 Strike rate (domestic/foreign) X $1.80 X £0.5556 Domestic interest rate (% p.a.) rd 1.45% rd 4.53% Foreign interest rate (% p.a.) rf 4.53% rf 1.45% Time (years, 365 days) T 0.493 T 0.493 Days equivalent 180 180 Volatility (% p.a.) s 9.40% s 9.40% Call option premium (per unit fc) c $0.07 c £0.0091 Put option premium (per unit fc) p $0.03 p £0.0207 (European pricing) Call option premium (%) c 3.73% c 1.70% Put option premium (%) p 1.64% p 3.87% Call option premiums for a U.S.-based firm buying call options on the British pound: 180-day maturity ($/pound) $0.07 90-day maturity ($/pound) $0.07 Difference ($/pound) $0.00 The maturity doubled while the option premium rose only about 4%.Explanation / Answer
Soln : Initially the price of the call option = $0.07
Let's calculate when maturity rose from 90 days to 180 days.
Prameters given , r = 1.45%, std. = 9.40%, t = 0.493, S0 = 1.87, X = 1.80
As per black scholes equation , the call option value
C = S0 *N(d1) - N(d2) *X *e-rt
d1 = (ln(S/K) + (std2/2 +r)*t)/s*t0.5 = (0.038152 + 0.493*(0.004418+1.45%)) /0.094*0.493 = 0.719
d2 = d1 - std*t0.5 = 0.719 - 0.066 = 0.653
Clculate N(d1) & N(d2) using the z table
C = 1.87*0.7642 - 1.80*e-0.0145*0.493*0.7422 = 0.102
For 90 days the call premium calculated in similar way only difference is t = 0.493/2 = 0.2465
We get C = 0.0845
.The maturity doubled while the call option premium rose about = (0.102-0.0845)/0.0845 = 20.64%