Outperformance Option Valuation

A company issues an option grant with an outperformance feature, against the S&P 500. Assume S&P 500 = 1100, S = 46, k = 45, s = 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?

 

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