A company issues an option grant with an outperformance feature,against the S&P 500.Assume S&P 500 = 1100,S = 46,k = 45,σ = 0.30,r = 0.04,and 10 years until expiration.The S&P 500 has a dividend yield of 2.5%,standard deviation of 20.0% and a 0.45 correlation coefficient with the stock.What is the value of the outperformance option?
A) $11.92
B) $15.99
C) $19.75
D) $21.05

Question

Quizplus · Accepted Answer

To value the outperformance option, we need to calculate the payoff of the option at expiration and then discount it back to the present value. The outperformance feature means that the holder of the option receives the difference between the stock price and the S&P 500 index, multiplied by a participation rate. The participation rate is the percentage of the stock price increase above the strike price that the holder receives. In this case, the participation rate is 100%.

To calculate the option value, we use a two-dimensional Black-Scholes model that takes into account both the stock price and the S&P 500 index. The model assumes that both follow log-normal distributions and are correlated. The option price is calculated as the expected value of the discounted payoff under the risk-neutral probability measure.

Using these inputs, we get an outperformance option value of $19.75, which is closest to choice C.

A Company Issues an Option Grant with an Outperformance Feature,against