Question

The stock of Nugents Nougats currently sells for $45 and has an annual standard deviation of 46 percent. The stock has a dividend yield of 5.4 percent and the risk-free rate is 5.4 percent. What is the value of a call option on the stock with a strike price of $41 and 46 days to expiration?

Answer 1

We can apply Black Scholes option pricing to calculate the value of call option.

if C is the call option price, then C=S*e^(-q*t)*N(d₁) -X*e^(-r*t)N(d₂), here N(x) is the standard normal cumulative distribution function.

S=$45,X=$41,q=0.054(assuming continuous compounding dividend rate), r=0.054(assuming continuous compounding risk-free rate),t=46/365=0.126

d₁ =[ln(S/X)+t*(r-q+?^2)]/[?*(t^0.5)] , where ?=annual std. deviation

so, d₁ =[ln(45/41)+0.126*(0.054-0.054+0.46^2)]/[0.46*(0.126^0.5)] =0.1197/0.1633 =0.73

From cumulative normal distribution table we get N(0.73) =0.7673

now d_{2 ⁼}d_1^- ?*(t^0.5) = 0.73 - [0.46*(0.126^0.5)] =0.73 - 0.1633 =0.5667

From cumulative normal distribution table we get N(0.57) =0.7157

now, C = 45*e^(-0.054*0.126)*0.7673 - 41*e^(-0.054*0.126)*0.7157 =34.2937 - 29.1442 =5.1495

So, the value of a call option on the stock with a strike price of $41 and 46 days to expiration is $5.15