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please provide accurate and complete solutions. Consider a three-month European

ID: 2738178 • Letter: P

Question

please provide accurate and complete solutions.

Consider a three-month European call option on XYZ stock whose strike price is not fixed but will be equal to 90% of the stock price at maturity. Note that this option is guaranteed to finish in-the-money. Suppose that ABC stock is currently trading at $100. Suppose no dividends are expected on the stock over the next three months. What is the arbitrage-free value of this call? Suppose a dividend of $4 is expected on ABC stock after one month. How would your answer to Part 1 change? Think of replication.

Explanation / Answer

a) Replicate the call with Long position in the Risk free Bond with face value X(Strike price) + short position in the stock.

Thus at maturity the payoff from the portfolio=ST-X=ST-0.90*ST=0.10*ST

The present cost of the portfolio

=arbitrage free value of call

=present value of 0.10*ST

=0.10*Stock's present value

=0.10*$100=$10

b)The dividend would reduce the Stock's present value by the present value of the Dividend therefore the value of the call shall reduce.