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Derivatives Securities and Markets

Problem Set: Determination of Futures and Forward Price

Question #a

Consider a six-month forward contract on a non-dividend paying stock. Assume the current stock price is $50 and the risk-free interest rate is 7.84% per annum with continuous compounding. Suppose the price of this six-month forward price is $53.50.

Show that it creates an arbitrage opportunity? Write down the complete strategy for an arbitrageur --- you must list down all the actions that are required now and later and demonstrate how arbitrageur earns a risk-less profit.  

Question #b

The two-month interest rates in Switzerland and the United States are 1% and 2% per annum, respectively, with continuous compounding. The spot price of the Swiss franc is $1.0600. The futures price for a contract deliverable in two months is $1.0500. Does it create any arbitrage opportunity? If yes, list down your strategy for setting up the arbitrage.   

Question #c

You are considering taking a short position in one-year futures on a stock. The stock is expected to pay two dividends; each dividend is $4 per share; first dividend is to be paid in four months, and the second dividend is paid in ten months. The current stock price is $100, and the risk-free rate of interest is 10% for all maturities. What should be one-year futures price contract?  

Question #d

A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock.

i. What are the forward price and the initial value of the forward contract?

ii. Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the original forward contract?