Question

A non-dividend paying stock sells for $110. A call on the stock has an exercise price of $105 and expires in 6 months. If the annual interest rate is 11% (0.11) and the annual standard deviation of the stock’s returns is 25% (0.25), what is the price of a European put option according to the Black-Scholes-Merton option pricing model.

A call and put expire in 0.41 year and have an exercise price of $100. The underlying stock is worth $90 and has a standard deviation of 0.25. The annual risk-free rate is 11 percent. The annual dividend yield (q) on the stock is 2%. The put option price from the three-period binomial model is:

Answer 1

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Answer:

1)

2)

As per Black Scholes Model
Value of put option = N(-d2)*K*e^(-r*t)-(S*e^(q*t))*N(-d1)
Where
S = Current price =		90
t = time to expiry =		0.41
K = Strike price =		100
r = Risk free rate =		11.0%
q = Dividend Yield =		2%
σ = Std dev =		25%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(90/100)+(0.11-0.02+0.25^2/2)*0.41)/(0.25*0.41^(1/2))
d1 = -0.34763
d2 = d1-σ*t^(1/2)
d2 =-0.34763-0.25*0.41^(1/2)
d2 = -0.507708
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.635941
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.694171
Value of put= 0.694171*100*e^(-0.11*0.41)-90*e^(-0.02*0.41)*0.635941
Value of put= 9.467