Question

Assume an option on a non-dividend paying stock when the stock price is £52, the strike price is £50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum and the time-to-maturity is three months.
a) Assuming that the option is a European call option, use the Black-Scholes formula to find the value of the option (the option premium).

b) Assuming that the option is an American call option, can you use the Black-Scholes formula to determine the option premium? Why or why not?
c) Assuming that the option is a European put option, use the Black-Scholes formula to determine the value of the option.

Answer 1

a) Assuming that the option is a European call option, use the Black-Scholes formula to find the value of the option (the option premium). = $5.06

b) Assuming that the option is an American call option, can you use the Black-Scholes formula to determine the option premium? Why or why not?

Black Scholes model cannot be used to calculate value of american options because the american options can be exercised before maturity and the american options will have arbitrage opportunities which doesnot satisfy the assumption of black Scholes model.

c) Assuming that the option is a European put option, use the Black-Scholes formula to determine the value of the option. = $1.58

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