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 rated(0,4)? (Recall that interest rates are always quoted on an annual basis unless

stated otherwise.)

Please submit your answer rounded to three decimal places. So for example, if your answer is0.4567then you should submit an answer of0.457.

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.)

Please submit your answer as a percentage rounded to two decimal places. So for example, if your answer is4.567%or equivalently0.04567, then you should submit an answer of4.57.

3.Hedging using futures

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

harvest and sale as150,000pounds of orange juice in3

months time. Suppose each orange juice futures contract is for15,000

pounds of orange juice, and the current futures price isF0=118.65cents-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.

Please submit your answer in cents-per-pound rounded to two decimal places. So for example, if your answer is123.456, then you should submit an answer of123.47.

4.Minimum variance hedge

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

harvest and sale as150,000pounds of grapefruit juice in3

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 for15,000

pounds of orange juice and the current futures price isF0=118.65cents-per-pound.

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

orange juice and grape fruit juice is20%and25%, respectively,

and the correlation coefficient is0.7. What is the approximate number

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

Please submit your answer rounded to the nearest integer. So for example, if your calculations result in 10.78 contracts you should submit an answer of 11.

5.Call Options

Consider a1-period binomial model withR=1.02,S0=100,

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

with strikeK=102. The stock does not pay dividends.

Please submit your answer rounded to two decimal places. So for example, if your answer is3.4567then you should submit an answer of3.46.

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?

Please submit your answer rounded to three decimal places. So for example, if your answer is43.4567then you should submit an answer of43.457.