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Homework #1
FIN4420A
Derivatives and Risk Management
1 A $50 stock pays a $1 dividend every 3 months, with the first dividend coming 3 months from today. The continuously compounded risk-free rate is 6%.
a. What is the price of a prepaid forward contract that expires 1 year from today, immediately after the fourth-quarter dividend?
b. What is the price of a forward contract that expires at the same time?
2. Suppose the current stock price is $35 and the continuously compounded interest rate is 5%.
a. What is the 6-month forward price, assuming dividends are zero?
b. If the 6-month forward price is $35.50, what is the annualized forward premium, i.e., annualized percent of ratio F0,T ÷ S0?
c. If the forward price is $35.50, what is the annualized continuous dividend yield.?
3. The spot price for an index is 1100, the risk-free rate is 5%, and the continuous yield on the index is 2%.
a. Suppose you observe a 6-month forward price of 1120. What arbitrage action would you take?
Ft0=S0e^
b. Suppose you observe a 6-month forward price of 1110. What arbitrage action would you take?
4. An index spot price is 1100 and the continuously compounded risk-free rate is 5%. You observe a 6-month forward price of 1129.257.
a. What dividend yield is implied by the forward price?
b. Suppose you believe the dividend yield over the next 9 months will be only 0.5%. What arbitrage action would you take?
c. Suppose you believe the dividend yield will be 3% over the next 9 months. What arbitrage action would you take?
5. The price of gold is currently $600 per ounce. Forward contracts are available to buy or sell gold at $800 for delivery in one year. The interest rate to lend or borrow money is 10%. What arbitrage action would you take?
6. A long forward contract on a non-dividend paying stock was entered into some time ago. It currently has 6 months to maturity and the risk-free rate (continuously compounded) is 10%. The stock’s current price is $25. The forward price that governs the transaction in 6 months under the forward contract is $24. What is the current value of the forward contract?
If someone answers all of these I will paypal them 15$.
Thanks
Sean
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