1a) Suppose the exchange rate is $1.75/£, the British pound-denominated continuo

Question

1a) Suppose the exchange rate is $1.75/£, the British pound-denominated continuously compounded interest rate is 4%, the U.S. dollar-denominated continuously compounded interest rate is 5%, and the exchange rate volatility is 21%. What is the Black-Scholes value of a 9-month $1.80-strike European call on the British pound?

Answers:

a.

$0.1429

b.

$0.1194

c.

$0.1574

d.

$0.1074

e.

$0.0000

· 1b)

Let S = $49, s = 40%, and r = 5.5% (continuously compounded). The stock is set to pay a single dividend of $1.30 nine months from today, with no further dividends expected this year. Use the Black-Scholes model (adjusted for the dividend) to compute the value of a one-year $50-strike European put option on the stock.

Answers:

a.

$8.49

b.

$7.32

c.

$6.81

d.

$7.75

e.

$5.51

1a) Suppose the exchange rate is $1.75/£, the British pound-denominated continuously compounded interest rate is 4%, the U.S. dollar-denominated continuously compounded interest rate is 5%, and the exchange rate volatility is 21%. What is the Black-Scholes value of a 9-month $1.80-strike European call on the British pound?

Answers:

a.

$0.1429

b.

$0.1194

c.

$0.1574

d.

$0.1074

e.

$0.0000

Explanation / Answer

Soln : a) Let S be the current price , S = $1.75/£ and K = strike price of the call option = $1.80/£

So as per the Black Scholes formula for currency option , C = S*e-F*T *N(d1)- K*e-DT *N(d2)

N (d) = cumulative distribution value

where F = Foreign interest rate = 4%, D = domestic interest rate = 5%, d1 = (ln(S/K) + (D-F+s2/2)*t)/s*t0.5

d2 = d1 - s*t0.5, here , t = T = 9 months= 9/12 = 0.75 and s = exchange rate volatility = 21%

Step calculate value of d1 and d2 , d1 = ((ln(1.75/1.80)+(1%+21%2/2)*0.75)/0.21*0.750.5

On solving we get d1 = -0.02273 and d2 = d1 - 0.21*0.750.5 = -0.20459

Step 2: Calculate N(d1) and N(d2) . So, N(-0.02273) = 1-N(0.02273) = 1-0.5088 = 0.4912

N(d2) = N(-0.20459) = 1- N(0.20459) = 1-0.5801 = 0.4199

Step3: Put these value in black scholes eqn : C = 1.75 *e-0.04*0.75* 0.4912 - 1.80*e-0.05*0.75*0.4199 = $0.1062

Value of call option = $0.1062 approx. equal to the option d = 0.1074

b) As here we need to calculate option value put with dividend payment one time, whose discounted value will be subtracted from the current price

So, P = -(S-D*e-r*T) *N(-d1)+ K*e-rT *N(-d2), here D = dividend

d1 = (ln((S-D*e-r*T)/K) + (r+s2/2)*t)/s*t0.5 = 0.16, d2 = 0.16 - 0.4*0.750.5 = -0.187

P = 50*e-(0.055*0.75)*N(0.187) - 47.75 *N(-0.16) = 50*0.9595*0.5742 - 47.75*0.4364 = $6.71

It is nearest to the value = $6.81, option c is correct.

d2 = d1 - s*t0.5

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