34. Using a closed-form solution, price the up-and-in put option with the following parameters: S = 100, K = 100, barrier H = 110, rebate of 50, maturity of one year, annual risk-free interest rate of 3%, and stock volatility of 40%. There are no dividends.
(a) What is the price of the option?
(b) What is the option price if the stock rises to 105?
(c) What is the option price if the stock rises to 109?
(d) What can you say about the sign of the delta and the gamma?
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