Question

The S&P 500 index currently stands at 2,700 and has a volatility of 11%. The risk-free interest rate is 2% and the dividend yield on the index is 4%.

a.) Use Black-Scholes to value a three-month European put option with a strike price of 2,500.

b.) Use Black-Scholes to value a one-year European call option with a strike price of 3,000.

Answer 1

a) Put option with strike price of 2500

Value of a put option as per Black-Scholes model is as follows -

Where, P = value of put option, X = strike price, r = continuously compounded risk free rate, t = time till maturity, S₀ = current market price, q = dividend yield

Also, d₁ and d₂ can be computed as follows -

So, first we compute d₁ and d₂ and then move on from there with each of the variables. Here is the solution -

b) Call option with strike price 3000

Call option as per Black-Scholes model is computed as follows -

where, C = value of call option, X = strike price, r = continuously compounded risk free rate, t = time till maturity, S₀ = current market price, q = dividend yield

Also, d₁ and d₂ formula is same as before. Here is the solution -

Let me know in case of any queries.