IEOR 4700-Term structure of interest rates and swap valuation

IEOR 4700-Term structure of interest rates and swap valuation

Subject: Business    / Finance   
Question

1. Term structure of interest rates and swap valuation

Suppose the current term structure of interest rates, assuming annual compounding, is as follows:
s1    s2    s3    s4    s5    s6
7.0%    7.3%    7.7%    8.1%    8.4%    8.8%

What is the discount rate d(0,4)? (Recall that interest rates are always quoted on an annual basis unless

stated otherwise.)

2. Swap Rates

Suppose a 6-year swap with a notional principal of $10 million is being

configured. What is the fixed rate of interest that will make the value

of the swap equal to zero. (You should use the term structure of interest rates from Question 1.)

3. Hedging using futures

Suppose a farmer is expecting that her crop of oranges will be ready for

harvest and sale as 150,000 pounds of orange juice in 3

months time. Suppose each orange juice futures contract is for 15,000

pounds of orange juice, and the current futures price is F0=118.65 cents-per-pound.

Assuming that the farmer has enough cash liquidity to fund

any margin calls, what is the risk-free price that she can guarantee herself.

4. Minimum variance hedge

Suppose a farmer is expecting that her crop of grapefruit will be ready for

harvest and sale as 150,000 pounds of grapefruit juice in 3

months time. She would like to use futures to hedge her risk but unfortunately there

are no futures contracts on grapefruit juice. Instead she will use orange juice futures.

Suppose each orange juice futures contract is for 15,000

pounds of orange juice and the current futures price is F0=118.65 cents-per-pound.

The volatility, i.e. the standard deviation, of the prices of

orange juice and grape fruit juice is 20% and 25%, respectively,

and the correlation coefficient is 0.7. What is the approximate number

of contracts she should purchase to minimize the variance of her payoff?

5. Call Options

Consider a 1-period binomial model with R=1.02, S0=100,

u=1/d=1.05. Compute the value of a European call option on the stock

with strike K=102. The stock does not pay dividends.

6. Call Options II

When you construct the replicating portfolio for the option in the previous question how many dollars do you need to invest in the cash account?