Question

Consider a one-year European call option on a stock when the stock price is $30, the strike price is $30, the risk-free rate is 5%, and the volatility is 25% per annum. Calculate the price and delta of the option.

Answer 1

To calculate the price of the European call option, we can use the Black-Scholes model. The formula for a European call option is: C = S * N(d1) - X * e^(-r * T) * N(d2). To calculate the delta of the option, we can use the formula: Delta = N(d1). For the given stock price, strike price, risk-free rate, and volatility, the price of the option is $10.77 and the delta is 0.6994.

Step-by-step explanation:

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

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

where:

• C is the price of the call option
• S is the current stock price ($30)
• N(d1) and N(d2) are the probabilities of the stock price reaching the strike price, calculated using the cumulative distribution function of the standard normal distribution
• X is the strike price ($30)
• r is the risk-free interest rate (5%)
• T is the time to expiration (1 year)

To calculate the delta of the option, we can use the following formula:

Delta = N(d1)

Substituting the given values into the formulas, we get:

C = 30 * N(0.525) - 30 * e^(-0.05 * 1) * N(0.275) = 10.77

Delta = N(0.525) = 0.6994