Question: Assume the Black-Scholes framework. You are given: (i) The current stock price is 100. (ii) The stock pays dividends continuously at a rate proportional to

Assume the Black-Scholes framework. You are given:

(i) The current stock price is 100.

(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2%.

(iii) The volatility of the stock is 20%.

(iv) The price of a 6-month European gap call option on the above stock with a strike price of 90 and a payment trigger of 110 is 7.3528.

(v) The price of a 6-month European gap put option on the above stock with a strike price of 90 and a payment trigger of 110 is −3.4343.

Ryan has just written 10 gap call options in (iv), and he delta-hedged his position immediately with shares of the stock.

After one month, the stock price drops to 95 and the price of the gap call option decreases to 4.2437.

Calculate the one-month holding profit for Ryan.

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