Final answer:
To calculate the value of a call option, you can use the Black-Scholes option pricing model. The formula takes into account factors such as the current stock price, exercise price, risk-free interest rate, time to expiration, and standard deviation of stock returns. By plugging in the given values into the formula, you can calculate the value of the call option. For part b, you would use a different exercise price in the calculations.
Step-by-step explanation:
To calculate the value of a call option, we can use the Black-Scholes option pricing model. The formula is as follows:
C = S₀e^(rT)N(d₁) - Xe^(-rT)N(d₂)
Where:
- C = value of the call option
- S₀ = current price of the stock ($70)
- X = exercise price of the option ($50)
- r = risk-free interest rate (6% or 0.06)
- T = time to expiration in years (1 year)
- N() = cumulative standard normal distribution function
- d₁ = (ln(S₀/X) + (r + σ²/2)T) / (σ√T)
- d₂ = d₁ - σ√T
- σ = standard deviation of the stock's returns
Given the information provided, we can calculate the value of the call option:
d₁ = (ln(70/50) + (0.06 + σ²/2) * 1) / (σ * √1)
d₂ = d₁ - σ * √1
Once you have calculated d₁ and d₂, you can use them in the Black-Scholes formula to find the value of the call option.
For part b, you would repeat the calculations using an exercise price of $65 instead of $50.