1.Suppose an investor underwrites a gas call option with a strike price of $3.00/MMBtu.

a.Does the investor face any price risk? Why or why not?

b.If the investor faces a risk, how can she hedge the risk? Explain.

2.The initial margin for the natural gas futures contract is $2400 and the maintenance margin is $1400. A company just bought two contracts at $3.15/MMBtu and the margin requirements were fulfilled.

a.At what price the company will be able to withdraw $4000 from the margin account?

b.At what price will the company receive a margin call?How much will the margin call be?

3.The company took a short position in a futures contract to sell 5000 barrels of oil in March 2018 for $40.00/Bbl. The contract was entered in March 2016. Suppose in December 2016, the oil price was $54.00 and it was $63.00 in December 2017 and $65.00 in march 2018.

a.Show the company's profit or loss on the contract?

b.What is the accounting and tax treatment of the transaction if the company is classified as (a) a hedger and (b) a speculator?

4.An investor holds 50,000 shares of a certain stock in April. The market price is $31 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P 500 futures contract. The index is currently 1,450 and one contract is for delivery of $53 times the index. The beta of the stock is 1.4. What specific strategy should the investor follow (you need to specify what positions the investor needs to take and the amount of the contract)?

5.Suppose the natural gas futures price for gas delivered in 6 months is $3.31, the interest rate is 5% per annum compounded quarterly. The gas storage cost is 4% per annum compounded continuously. There is no convenience yield. The current spot gas price is $3.52.

a.Is there an arbitrage opportunity? Why?

b.If there is an arbitrage opportunity, what should the profitable strategy be? How much is the profit?

c.Suppose there is a convenience yield and there is no arbitrage opportunity, what is the convenience yield?

6.A stock is expected to pay a dividend of $3 per share in two months and in five months. The stock price is $51, and the risk-free rate of interest is 5% per annum with continuous compounding for all maturities. An investor has just taken a long position in a six-month forward contract on the stock.

a.What are the forward price and the initial value of the forward contract?

b.Three months later, the price of the stock is $55 and the risk-free rate of interest is still 5% per annum. What are the forward price and the value of the long position in the forward contract?

7.Suppose a European call option on oil has a strike price of $101 and an expiration date in two months. The price of the call is $21. The risk-free interest rate is 5% per annum, the current spot price is $111.

a.Identify the arbitrage opportunity open to a trader. What is the correct strategy to take advantage of the arbitrage opportunity? You need to calculate the present value of the profit to the arbitrageur if there is an arbitrage opportunity.

b.What's going to happen to the prices of the call and spot as the result of the arbitrage? Why?

Optimal hedge ratio

Number of contract to hedge the risk in a portfolio:

Changing beta:

Short:when,

Long:when,

Forward and spot relationship:F₀= S₀e^rT

CAPM model:r_i= r_f+ b(r_m- r_f), where r_iis company return, r_fis risk free rate,r_mis market return, b is the beta

Converting different compounding:

Values of forward contract: =S₀- Ke^-rT, =S₀-I - Ke^-rT, =S₀e^-qT- Ke^-rT,

Futures price for investment asset:F₀=S₀e^(r-q)T

Futures price convenience yield included:F₀=S₀e^(r+u-y)T

Lower bound for European call option:c>=S₀-Ke^-rT, put option:p>=Ke^-rT-S₀