Find the input d₁ of the Black-Scholes price of a six-month call option on Japanese yen.The strike price is $1 = ¥100.The volatility is 25 percent per annum; r_$ = 5.5% and r_¥ = 6%. A)d₁ = 0.074246 B)d₁ = 0.005982 C)d₁ = $0.006137/¥ D)none of the options

Question

Quizplus · Accepted Answer

Using the Black-Scholes formula, we have:

d1 = [ln(S/K) + (r+S12U1B2/2)t] / (S12U1B2t)
= [ln(1/100) + (0.055+0.25/2)0.5] / (0.25*0.5)
= -1.440604

d2 = d1 - S12U1B2t 
= -1.440604 - 0.25*0.5
= -1.565302

N(d1) = 0.074246 (from normal distribution table)

N(d2) = 0.065972 (from normal distribution table)

Therefore, the Black-Scholes price of the call option is:

C = SN(d1) - Ke-rS1U1B1tN(d2)
= 1*N(0.074246) - 100*exp(-0.06*0.5)*N(0.065972)
= $0.005982 or ¥0.5982

So the input dS1U1B11S1U1B0 is 0.074246.

Find the Input D1 of the Black-Scholes Price of a Six-Month

Find the Input D₁ of the Black-Scholes Price of a Six-Month