enter a long position in a 10-year forward contract on a non-dividend-paying stock. The stock price is $50 and the risk-free rate of interest is 5% per annum with yearly compounding (as per 1st of January 2023).
Suppose that you, on 1st of January 2023, enter a long position in a 10-year forward contract on a non-dividend-paying stock. The stock price is $50 and the risk-free rate of interest is 5% per annum with yearly compounding (as per 1st of January 2023).
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a) What are the forward price and the initial value of the forward contract?
Five years later, 1st of January 2028, the price of the stock is $60 and the risk-free interest is still 5%.
b) On 1st of January 2028, what are the forward price and the value of the forward contract that you entered into on 1st of January 2023? Explain.
- c) Suppose that you on 1st of January 2028 enter a short position in a forward contract on the same underlying stock and with expiration date in 5 years. What is the value of your total position? (I.e. what is the total value of the long position in the forward contract in a) and your short position). What is the payoff of your total position at maturity?
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d) On 1st of January 2028, what is the value to the party holding the short position in the contract entered into on 1st of January 2023? Explain.
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e) What is an arbitrage opportunity? Discuss using an example (of your choice) and explain how an investor may exploit it to make (infinitely) large profits.
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