Question

The HSBC stock price is currently trading at $200. You believe that HSBC will have an expected return of 8% with volatility of 24.1% per year, while annual interest rates with annual compounding are at 0.95% (R). Explain the concept on how to compute the price of an European put on HSBC with a strike price of $200 and maturity of 1 year?

Answer 1

As per Black Scholes Model
Value of put option = N(-d2)*K*e^(-r*t)-(S)*N(-d1)
Where
S = Current price =		200
t = time to expiry =		1
K = Strike price =		200
r = Risk free rate =		0.95%
q = Dividend Yield =		0%
σ = Std dev =		24.1%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(200/200)+(0.0095-0+0.241^2/2)*1)/(0.241*1^(1/2))
d1 = 0.159919
d2 = d1-σ*t^(1/2)
d2 =0.159919-0.241*1^(1/2)
d2 = -0.081081
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.436472
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.532311
Value of put= 0.532311*200*e^(-0.0095*1)-200*0.436472
Value of put= 18.16