# Finance.

Introduction to Derivative Securities

1.Question 1
Term structure of interest rates and swap valuation Suppose the current term structure of interest rates, assuming annual compounding, is as follows:
s_1s 7.0%
s_2s 7.3%
s_3s 7.7%
s_4s 8.1%
s_5s 8.4%
s_6s 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.Question 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.Question 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 F 0=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.Question 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 F 0=118.65 cents-per-pound.
The volatility, i.e. the standard deviation, of the prices of
orange juice and grape fruit juice is 20\%20% and 25\%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?
(edited 4 years ago)
3.Question 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 F 0=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.