Question

A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $51

Answer 1

To calculate the value of the European call option, we can use the Black-Scholes formula. The formula for the value of a European call option is: C = S * N(d1) - X * e^(-r * T) * N(d2), where S is the current stock price, X is the strike price, r is the risk-free interest rate, and T is the time to expiration.

Step-by-step explanation:

To calculate the value of the European call option, we can use the Black-Scholes formula. The formula for the value of a European call option is:

C = S * N(d1) - X * e^(-r * T) * N(d2)

where:

• C is the value of the call option
• S is the current stock price
• N(.) is the cumulative distribution function of the standard normal distribution
• d1 and d2 are calculated using the following equations:

d1 = (ln(S/X) + (r + (σ^2)/2) * T) / (σ * sqrt(T))

d2 = d1 - σ * sqrt(T)

In this case, the current stock price (S) is $50, the strike price (X) is $51, the risk-free interest rate (r) is 5% per annum with continuous compounding, and the time to expiration (T) is 6 months. The volatility (σ) is not provided in the question, so we cannot calculate the exact value of the option without this information.