Question

An index currently stands at 736 and has a volatility of 27% per annum. The risk-free rate of interest is 5.25% per annum and the index provides a dividend yield of 3.65% per annum. Calculate the value of a five-month European put with an exercise price of 730.

Answer 1

The value of a put option is given by the Black Scholes model

The dividend yield is 3.65% per annum

Continuously compounded divided yield = ln(1.0365) = 3.58%

where S is the dividend-adjusted current price = 736*e^(-0.0358*5/12) = $725.2

K is the strike price = $730

Risk free rate r = 0.0525

Volatility = 0.27

Time to maturity t = 5/12

d1 = (ln(725.2/730) + (0.0525+ (0.27*0.27/2))*(5/12))/(0.27*(5/12)^0.5) = 0.181

d2 = 0.181 - 0.27*(5/12)^0.5 =0.008

N(-d1) = 0.428

N(-d2) = 0.497

Substituting, we get

p = (730*0.497*e^(-0.0525*5/12)) - 725.9*0.428 = 44.3

Hence the price of a 1-year put option c = $44.3