Question: Assume the Black-Scholes framework. You are given: (i) The current price of the P&K 777 index is 500. (ii) The P&K 777 index pays dividends

Assume the Black-Scholes framework.

You are given:

(i) The current price of the P&K 777 index is 500.

(ii) The P&K 777 index pays dividends continuously at a rate proportional to its price. The dividend yield is 2%.

(iii) The continuously compounded risk-free interest rate is 6%.

(iv) The current prices and volatility of futures contracts on P&K 777 of various maturities:

Maturity (in Years) Current Price Volatility 1 520.41 2 541.64 30% 3 563.75 4 586.76

Calculate the price of a 2-year 550-strike European put option on a 1-year futures contract (i.e., the futures matures at the end of 3 years).

Maturity (in Years) Current Price Volatility 1 520.41 2 541.64 30% 3 563.75 4 586.76

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