Suppose S = $52.50,K = $50,σ = 0.25,r = 0.04 and div = 0.01.What is the price of a gap option with 156 days until expiration and K₁ = $32.00?

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Quizplus · Accepted Answer

A gap option is a type of exotic option where the payoff depends on the difference between the asset price at expiration and a specified price level (K₁), provided the asset price is beyond a certain level (K). The price of a gap call option can be calculated using the Black-Scholes formula with some modifications. Given the parameters: S (current stock price) = $52.50, K (strike price) = $50, σ (volatility) = 0.25, r (risk-free interest rate) = 0.04, div (dividend yield) = 0.01, T (time to expiration in years) = 156/365, and K₁ (specified price level) = $32.00, the correct price of the gap option is $16.00. This calculation involves using the modified Black-Scholes model to account for the gap feature, which is not provided in the question but is a standard approach for pricing such options.