Financial Engineering Question

MF650

Assignment 2

1. Lalaa Corp. wants to invest its cash surplus of $1m. in a GIC (i.e., certificate of deposits) for a period of 6 months. The best GIC rate that it could find is 5.5% p.a. continuous compounding. [Note: This is the rate that Lalaa can lend its money. It is not its borrowing rate. Nor is it anybody else's lending or borrowing rate.] Mr. Dipsey, the company's treasurer, has asked you to explore the possibility of creating a synthetic lending transaction by a portfolio of options and stocks. You observed the following information :

Security Price

6-month European call whose exercise price = $32 $2.10

6-month European put whose exercise price = $32 $2.92

the underlying (non- dividend- paying) stock $30

Based on the above observations, will Lalaa be better, please also show how it can be created.

2. What is the value of a European call on a non-dividend-paying stock that has a very long maturity (say, 1,000 years)? What about a n American call with an infinite maturity? [Hint: Compare the upper bound and lower bound for option prices.]

3. Consider a 2-month European call whose exercise prices is $101. The current stock prices is $100 and its volatility is 20% p.a. The risk-free rate is 5% p.a. continuously compounding. The stock is expected to pay a dividend of $2 in one month's time.

a.) Using a two-period binomial tree, what is the value of a 2-month American call whose exercise price is a $101?

b.) Using a two-period binomial tree, what is the value of a 2-month American put whose exercise price is a $101?

4. An Average Price call is a type of Asian option that pays off max{0, Savg -X} at maturity where Savg is the average of the stock prices from the start of the call to its maturity. For example, consider the following path for stock prices:

Day Prices

0