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Question
In a financial market a stock is traded with a current price of 50. Next period the price of the stock can either go up with 30 per cent or go down with 25 per cent. Risk-free debt is available with an interest rate of 8 per cent. Also traded are European options on the stock with an exercise price of 45 and a time to maturity of 1, i.e. they mature next period.
1. Find prices of Arrow-Debreu securities.
2. Calculate the price of a call option by constructing and pricing a replicating portfolio.
3. Calculate the price of a put option by RNVR.
4. Does put-call parity hold? Explain.
5. Construct one long strap and one long straddle using any options from previous part. Sketch the profit and loss graph for each of your portfolios separately and explain the similarity and difference between two positions.
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