1) Consider a European call option on a currency. The exchange rate is 1.0000, the
strike price is 0.9100, the time to maturity is one year, the domestic risk-free rate is 5%
per annum, and the foreign risk-free rate is 3% per annum. What is a lower bound to the
option price? (Give four decimal places.)
2) An exchange rate has a volatility of 12%. The domestic and foreign risk-free interest
rates are both 4%, respectively. The time step on a binomial tree is three months.
What are the , and parameters for a Cox, Ross, and Rubinstein tree? Give four
decimal places
3) Fill in the blanks
In Mertons model the _ _ _ _ _ of a company is regarded as an option on the companys
_ _ _ _ _
4) What, to the nearest cent, is the lower bound for the price of a two-year European
call option on a stock when the stock price is $20, the strike price is $15, and the
risk-free interest rate with continuous compounding is 5% and there are no dividends?
5) The price of a European call option on a non-dividend-paying stock with a strike
price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate
(all maturities) is 6% and the time to maturity is one year. A dividend of $1 is expected
in six months. What, to the nearest cent, is the price of a one-year European put option
on the stock with a strike price of $50?
6) A call and a put on a stock have the same strike price and time to maturity. At
10:00am on a certain day, the price of the call is $3 and the price of the put is $4. At
10:01am news reaches the market that has no effect on the stock price or interest rates,
but increases volatilities. As a result the price of the call changes to $4.50. What would
you expect the price of the put to change to?
7) An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest
rates are 5% and 7% (both expressed with continuous compounding). What is the
six-month forward rate? Give four decimal places.
8) In a volatility smile diagram
i. What is plotted on the horizontal axis?
ii. What is plotted on the vertical axis?