assignment /essay/report/paper写作

### 25620 DERIVATIVE SECURITIES ASSIGNMENT

### ( 20 + 1 5 + 1 5 + 20 = 7 0 marks)

### DUE ON WEDNESDAY 6 JUNE 2018 (05:00PM)

### Please submit your assignment into the box labelled FINANCE 1 on level 5 of

### Building 8 (Dr Chau Chak Wing Building)

Congratulations, you have been hired as a financial analyst at the bank following your studies at the University of Technology Sydney. It is a significant honour to work for the leading investment bank and you have fought off tough competition for the job. The recruitment team selected you for your personable character, your analytical mind, your ability to solve problems, work in teams and get the job done. In your second week on the job, you have been asked to recall your knowledge from studying Derivative Securities to price such instruments and advise clients on hedging strategies and potential arbitrage opportunities. A summary of the lectures which will help you with these tasks include:

- Futures Pricing (Lecture 2 and 3)
- Option trading strategies (Lecture 7)
- Portfolio insurance (Lecture 10)
- Option pricing and hedging (Lectures 9 and 11 )

### [ 3 + 3 + 1 + 3 +4+4+ 2 = 20 marks]

Forward curves provide important information about the market conditions to traders and investors. You have been assigned to analyse the crude oil forward curves and to explain how price risk in these markets can be hedged with crude oil futures.

The NYMEX WTI light sweet crude oil futures prices traded on CME Group (Globex) on 29 March 2018 are presented at Table 1.

```
Table 1: NYMEX WTI light sweet crude oil futures prices on 29 March 2018
(Source: http://ifs.marketcenter.com/quick_reference.jsp)
```

(a) Plot the NYMEX WTI light sweet crude oil forward curve on 29 March 2018 and provide an explanation of the pattern of the forward curve. News announcements and online articles should be used to support your discussion.

On the 29 March 2018 , the spot crude oil price is USD 65.25 per barrel. Assume that the interest rate is 3.5% per annum with continuous compounding. The monthly storage cost for crude oil is estimated at 41 cents per barrel payable in advance.

(b) Calculate the convenience yield of the crude oil implied by the June 2018 and the December 201 8 futures contract (use Table 1). Round off the time to maturity to the nearest month (e.g. 3 months for the June 2018 contract and 9 months for the December 2018 contract).

(c) Interpret the convenience yields calculated in part (b).

```
It is now 29 March, 201 8. A crude oil producer will sell 10,000 barrels of crude oil in mid-June
2018. The crude oil company is concerned about the falling crude oil prices and they consider
to lock-in the price by using NYMEX WTI light sweet crude oil futures. The current spot crude
oil price is USD 65.25 per barrel. You have estimated that the quarterly standard deviation of
the spot crude oil price changes is 0. 564 , the quarterly standard deviation of the crude oil
futures price changes is 0. 521 , and the correlation coefficient between these price changes is
```

(d) Calculate the optimal number of contracts required (by tailing the hedge) and recommend an effective hedge. Use the appropriate futures contract from Table 1.

(e) Assume that the crude oil company is ready to sell crude oil in mid-June. In mid-June, the crude oil spot price has decreased to 54.00 USD per barrel and the crude oil futures price for delivery in one month is 52.50 US cents per barrel. Calculate the outcome with and without the hedge. What is the companys effective selling price with and without the hedge? Did the crude oil company benefit from this hedge?

(f) Assume that the producer is ready to sell crude oil in mid-June. In mid-June, the crude oil spot price has increased to 80.00 USD per barrel and the crude oil futures price for delivery in one month is 78.50 US cents per barrel. Calculate the outcome with and without the hedge. What is the companys effective selling price with and without the hedge? Did the company benefit from this hedge?

(g) Explain the main objective of the recommended hedge and why it cannot be a perfect hedge.

```
Additional Information
NYMEX WTI light sweet crude oil futures contract specifications (CBOT)
Trading Unit: 1 ,000 barrels
Tick Size: 0.01 USD per barrel
Initial Margin: 3,700USD Maintenance Margin: 2 , 100 USD
Contract Months: All
Last Trading Day: Trading in the current delivery month shall cease on the third business day prior
to the twenty-fifth calendar day of the month preceding the delivery month.
Settlement: Physical delivery
```

### ( 3 + 6 + 3 + 3 = 1 5 marks)

```
As a valued member of the UTS alumni, you have been asked to be a guest lecturer for Lecture
8 and 9 for Derivative Securities (25620). You have been asked to go through calculating
option prices using the binomial tree and Black-Scholes model.
```

```
The S&P 5000 is currently standing at 263 0, has a volatility of 20% per annum and a dividend
yield of 2. 5 % per annum with continuous compounding. The risk-free interest rate is 3. 10 %
per annum with continuous compounding. Given your expertise in index options you decide
to use a four-step binomial tree to calculate the following option prices (to four decimal
places):
```

(a) a six-month short forward contract on the index, with delivery price of 2650. Calculate also the theoretical value of the forward contract. Compare and comment.

(b) a European six-month put option with a strike of 2650. Calculate also the value of the option by using the Black-Scholes formula. Compare and comment.

(c) an American six-month put option with a strike of 2650.

(d) a European down-and-out barrier put option with a strike of 2650 and knockout barrier of 240 0 maturing in 6 months. A down-and-out put option gives the holder the right to sell the underlying asset at the strike price on the expiration date so long as the price of that asset did not go below a pre-determined barrier during the options lifetime. When the price of the underlying asset falls below the barrier, the option is "knocked-out" and no longer carries any value.

### ( 4 + 2.5 + 3 + 3 + 2.5 = 1 5 marks)

A client holds a well-diversified equity portfolio worth $ 120 ,000,000 with a beta of 1. 4 0. The dividend yield of the equity portfolio is 2. 8 % per annum with simple compounding. The client is concerned about a market downturn and he has requested your advice in protecting the value of the portfolio. Yet he is keen to benefit if the market moves favourably.

The S&P500 index is currently at 2,640 and the dividend yield of the S&P500 index is 2.3% per annum with simple compounding. The risk-free interest rate is 3.8% per annum with continuous compounding.

(a) Describe the options portfolio insurance strategy that would hedge the portfolio over the next four months (e.g. no losses will be made on the equity portfolio over the next four months). Available index options are quoted in increments of five index points. Explain why this strategy fulfils the clients request and why hedging with index futures does not suffice.

(b) Calculate the insurance premium. Assume that the volatility of the index is 2 0 % per annum and the dividend yields and the risk-free interest rate when expressed as simple rates are approximately the same as the continuously compounded rates.

To explain the benefits and issues associated with this hedging strategy, you calculate the gains/losses of the strategy under two scenarios:

(c) the level of the S&P500 index in four months is 2,0 00 ; (d) the level of the S&P500 index in four months is 3,0 00. (e) Prepare a 200 – word summary to discuss the outcome of the insurance strategy and make a recommendation.

### ( 3 + 4 + 6 + 7 = 2 0 marks)

Gold markets have been very volatile. An investor feels that it is a great opportunity to make profits by trading long strips (a strip involves buying two put options and one call option with the same strike and maturity).

The current price of gold is $1,326.8 per ounce and the six-month gold futures price is $1,339.30 per ounce. The investor wants to setup the strategy to purchase 2 00 strips (long 200 put options and long 4 00 put options) by using options on gold futures maturing in six months with a strike of $1,340. The volatility of the gold futures price is 20 %, and the risk-free interest rate is 3.5% p.a. with continuous compounding.

You have been assigned to compute the cost of the strategy to the investor and also to assess the risk to the investment bank and recommend suitable hedging strategies. You will need to compute the following:

(a) Calculate the premium cost of these trades to the investor.

(b) By constructing the table and diagram of the profit/loss of the strips, discuss the profit and loss potential of this strategy. What is the investor expectation on markets volatility and direction (bull or bear)?

(c) Evaluate the delta, the gamma and the vega of the strips positions to the investment bank. Interpret these numbers.

(d) The investment bank wants to hedge its exposure of the associated strips. A CME traded option of gold futures has a delta of 0. 43 , a gamma of 0. 009 and a vega of 3 50. (i) What position in the traded option and in gold futures would make the strips both delta and gamma neutral? (ii) What position in the traded option and in gold futures would make the strips both delta and vega neutral? (iii) What are the benefits of creating a delta neutral, gamma neutral and vega neutral position?