Question

What is the price of a six-month European call option on a stock expected to pay a dividend of $1.50 in two months when the stock price is $50, the strike price is $50, the risk-free interest rate is 5% per annum and the volatility is 30% p.a.? Show all working.

Answer 1

Solution:

Strike price = $50, Spot price = $50, Volatility = 30%, Risk-free rate = 5%, Time = 0.5 year

Dividend = 1.5 in 2 months

Present value of the dividend = 1.5 * exp(-5%*2/12) = 1.4876

Spot price Pv of dividend = $50 - 1.4876 = 48.5124

Using Black Scholes formula we can calculate the call option price

All the calculation are goiven in below excel image

The call option premium = 3.98