2214AFE - DerivativesSecurities - Management Assignment Help

Assignment Task

Part A: Calculation Questions 

Problem 1: Properties of Options 

The price of a European put that expires in six months and has a strike price of $100 is $3.59. The underlying stock price is $102, and a dividend of $1.50 is expected in four months. The term structure is flat, with all risk-free interest rates being 8% (cont. comp.). 
a. What is the price of a European call option on the same stock that expires in six months and has a strike price of $100?[1 marks] 
b. Explain in detail the arbitrage opportunities if the European callprice is $6.1. How much will be the arbitrage profit? [3.5 marks] 
c. Explain in detail the arbitrage opportunities if the European call price is $8.8. How much will be the arbitrage profit? [3.5 marks] 

Problem 2: Option Valuation (18 marks)
In this question, you need to price options with various approaches. You will consider puts and calls on a share. Please read following instructions carefully:
• The spot price of this share will be determined by your student number. You need to use the last digit of your student number. The spot price of the share will be (last digit of your student number*10+6). For example, if the last digit of your student number is 5, the spot share price will be 5*10+6=56. If the last digit of your student number is 0, please replace it with 4, i.e. the spot price will be 4*10+6=46.
• The strike price of the options will be the share price you just calculated +2. For example, if the share price you calculated based on your student number is 56, the strike price of the options will be (56+2)=58.
Based on this spot price and this strike price as well as the fact that the risk-free interest rate is 6% per annum with continuous compounding, please undertake option valuations and answer related questions according to following instructions:

Binomial trees:
Additionally, assume that over each of the next two four-month periods, the share price is expected to go up by 11% or down by 10%. 
a. Use a two-step binomial tree to calculate the value of aneight-month European calloption using the no-arbitrage approach. [2.5 marks] 
b. Use a two-step binomial tree to calculate the value of aneight-month European putoption using the no-arbitrage approach. [2.5 marks] 
c. Show whether the put-call-parity holds for the European calland the European putprices you calculated in a. and b.[1 mark] 
d. Use a two-stepbinomial tree to calculate the value of an eight-month European call option using risk-neutral valuation.[1 mark] 
e. Use a two-stepbinomial tree to calculate the value of an eight-month European put option using risk-neutral valuation. [1 mark] 
f. Verify whether the no-arbitrage approach and the risk-neutral valuation lead to the same results. [1 mark] 
g. Use a two-step binomial tree to calculate the value of an eight-month American put option. [1 mark] 
h. Calculate the deltas of the European put and the European call at the different nodes of the binomial three. [1 mark] 
Note: When you use no-arbitrage arguments, you need to show in detail how to set up the riskless portfolios at the different nodes of the binomial tree.

Black-Scholes-Merton model:
Using the information given above regarding the spot and strike price, risk-free rate of return and the fact that the volatility of the share price is 18%, answer following questions:
i. What is the price of an eight-month European call? [1 mark] 
j. What is the price of an eight-month American call? [1 mark] 
k. What is the price of an eight-month European put? [1 mark] 
l. How would your result from k. change if a dividend of $1 is expected in three months? How would your result fromk. change if a dividend of $1 is expected in ten months?[2 marks] 
Note for calculations with the BSM model: Keep four decimal points for d1 and d2. Use the Table for N(x) with interpolation in calculating N(d1) and N(d2).

Finally,
m. Compare the results you obtained for the prices of European puts and calls using binomial trees and Black-Scholes-Merton model. How large are the differences when expressed as a percentage of the spot price of the share? Provide a possible explanation for these differences.[2 marks]

Problem 3: Derivatives Valuation (6 marks)
A stock price is currently $36. During each three-month period for the next six months it is expected to increase by 9% or decrease by 8%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off(max[(40-ST),0])2where   is the stock price in six months. 
a. What are the payoffs at the final nodes of the tree? [1 mark]
b. Use no-arbitrage arguments (you need to show how to set up the riskless portfolios at the different nodes of the binomial tree).[2 mark]
c. Use risk-neutral valuation.[1 mark]
d. Verify whether both approaches lead to the same result.[1 mark]
e. If the derivative is of American style (ST in the payoff function refers to the stock price when the option is exercised), should it be exercised early? [1 mark]

Problem 4. Value at Risk [18 marks] 

This is a Bloomberg-based exercise. 

Suppose you hold a portfolio consisting of a $350,000 investment in company A stock and a $650,000 investment in company B stock. Companies A and B are ASX50 constituent companies. 

Rules for the choice of companies A and B.Company A is ranked as the sum of all the digits in your student number, and company B is ranked as the sum of the last two digits of your student number. The ranking is based on market cap, with 1 indicating the largest company at the ASX and 50 the fiftieth largest company. If the sum of all the digits, in case of A, is more than 50, you will choose the company with the rank of (the sum – 50). In case of B, if the sum is 0, you then choose the rank of 1. For example, if your student number is s9999888, company A should be ranked as (9+9+9+9+8+8+8)=60-50=10; company B should be ranked as 8+8=16. If your student number is s1234500, you should choose company A with the rank of (1+2+3+4+5+0+0)=15, and company B with the rank of (0+0)=0+1=1. Please provide a screenshot of the ranking list.
Once you identify the two companies, you can retrieve relevant data from Bloomberg. Please use the instructions available under L@G/Course contents/Bloomberg remote access and timetable. In your course site, there is a section called “Bloomberg Recordings”, where you can find some instruction videos which may be helpful to you in navigating the Bloomberg system. If you cannot access Bloomberg terminal, alternatively you can go to Yahoo! Finance to retrieve the relevant data. 

You can now start performing the following tasks: 
a. Search for the stocks of these two companies. Download historical daily price data over the last 501 trading days (approx. 2 years). [1 mark] 
b. Calculate with Excel the daily returns of the stocks of companies A and B. [1 mark]
Now you need to estimate VaR with the two approaches you learned in class.
Historical simulation:
c. Based on the 500 returns for each stock calculated in b., calculate 500 alternative scenarios for the $ value of the $350,000 investment in company A stock and the $650,000 investment in company B stock, respectively. Sum these two for each scenario to obtain 500 simulations for the $ value of your portfolio consisting of stock A and stock B. [2 marks] 
d. Based on the 500 scenarios for the $ value of your portfolio consisting of stock A and stock B, calculate the 500 alternative gains/losses for your portfolio.[1 marks] 
e. Calculate the 5-day 99% VaR for this portfolio. What does it mean? [2 marks]
f. Briefly discuss the advantages/disadvantages of this approach. [1 mark] 
Model-building approach:
g. Calculate the standard deviations of the stocks’ returns over the last two years. [1 mark] 
h. Calculate the coefficient of correlation between the stocks’ returns. [1 mark] 
i. Compute the 5-day 99% VaR for this portfolio. What does it mean? [2 marks] 
j. By how much does diversification reduce the VaR? Also provide a brief comment on the reduction. [2 marks] 
k. Briefly discuss the advantages/disadvantages of this approach. [1 mark] 
Finally, 
l. Compare the results of both approaches.Provide possible explanations for the differences.[2 marks] 
m. Briefly discuss the usefulness of VaR.[1 mark]

Additional submission requirements for problem 4:
• Additionally to your calculations, please insert in the Word file that you will submit the screenshots you have made showing companies which you have used. 
•  Upload the Excel file showing your data and calculations. 
Part B: Research component (20 marks)

Since derivatives markets have become very popular in the last fifty years, historyhas witnessed many spectacular examples of derivatives misuse which have resulted in large losses for financial and non-financial institutions. For this part of the assignment, you need to do some research. Identify one prominent example of a financial disaster caused by the misuse of derivatives. Explain in your own words in detail what went wrong and what was the result of the derivatives misuse. 

Furthermore, an investment guru, Warren Buffett, once referred derivatives to as "time bombs" and financial "weapons of mass destruction” (details can be found in the appendix).Please comment on his remark.  Do you agree with Buffet’s opinion? 

Part C: Oral presentation (30 marks)
This component of the assignment requires the submission of a pre-recorded oral presentation of 8 to 10 minutes.
In this presentation, please use Power Point slides and address the following two aspects.
1.  Please explainin your own words the two approaches you used for estimation of Value at Risk in Problem 4 from Part A. State the results you have obtained, compare and interpret them. What are the advantages and disadvantages of these two approaches for VaR estimation? Briefly discuss the usefulness of VaR.
This component of the oral presentation should take you no longer than 5 minutes.
2.  Please summarize the results from Part B of the assignment. Describe the example for a derivatives disaster you have chosen. Comment on Warren Buffet’s statement about derivatives and financial markets. 
This component of the oral presentation should take you no longer than 5 minutes.
Please follow the instructions provided on L@G/Assessment/Assignment to create and submit your presentation. 
Please ensure that your webcam is turned on so that your face is recorded as well and show clearly your student ID at the beginning of your presentation.
END OF ASSIGNMENT
Appendix: Warren Buffet on Derivatives

Following are edited excerpts from the Berkshire Hathaway annual report for 2002.
I view derivatives as time bombs, both for the parties that deal in them and the economic system.Basically these instruments call for money to change hands at some future date, with the amount to be determined by one or more reference items, such as interest rates, stock prices, or currency values. For example, if you are either long or short an S&P 500 futures contract, you are a party to a very simple derivatives transaction, with your gain or loss derived from movements in the index. Derivatives contracts are of varying duration, running sometimes to 20 or more years, and their value is often tied to several variables.

Unless derivatives contracts are collateralized or guaranteed, their ultimate value also depends on the creditworthiness of the counter-parties to them. But before a contract is settled, the counter-parties record profits and losses – often huge in amount – in their current earnings statements without so much as a penny changing hands. Reported earnings on derivatives are often wildly overstated. That’s because today’s earnings are in a significant way based on estimates whose inaccuracy may not be exposed for many years.

The errors usually reflect the human tendency to take an optimistic view of one’s commitments. But the parties to derivatives also have enormous incentives to cheat in accounting for them. Those who trade derivatives are usually paid, in whole or part, on “earnings” calculated by mark-to-market accounting. But often there is no real market, and “mark-to-model” is utilized. This substitution can bring on large-scale mischief. As a general rule, contracts involving multiple reference items and distant settlement dates increase the opportunities for counter-parties to use fanciful assumptions. The two parties to the contract might well use differing models allowing both to show substantial profits for many years. In extreme cases, mark-to-model degenerates into what I would call mark-to-myth.

I can assure you that the marking errors in the derivatives business have not been symmetrical. Almost invariably, they have favored either the trader who was eyeing a multi-million dollar bonus or the CEO who wanted to report impressive “earnings” (or both). The bonuses were paid, and the CEO profited from his options. Only much later did shareholders learn that the reported earnings were a sham.

Another problem about derivatives is that they can exacerbate trouble that a corporation has run into for completely unrelated reasons. This pile-on effect occurs because many derivatives contracts require that a company suffering a credit downgrade immediately supply collateral to counter-parties. Imagine then that a company is downgraded because of general adversity and that its derivatives instantly kick in with their requirement, imposing an unexpected and enormous demand for cash collateral on the company. The need to meet this demand can then throw the company into a liquidity crisis that may, in some cases, trigger still more downgrades. It all becomes a spiral that can lead to a corporate meltdown.

Derivatives also create a daisy-chain risk that is akin to the risk run by insurers or reinsurers that lay off much of their business with others. In both cases, huge receivables from many counter-parties tend to build up over time. A participant may see himself as prudent, believing his large credit exposures to be diversified and therefore not dangerous. However under certain circumstances, an exogenous event that causes the receivable from Company A to go bad will also affect those from Companies B through Z.
In banking, the recognition of a “linkage” problem was one of the reasons for the formation of the Federal Reserve System. Before the Fed was established, the failure of weak banks would sometimes put sudden and unanticipated liquidity demands on previously-strong banks, causing them to fail in turn. The Fed now insulates the strong from the troubles of the weak. But there is no central bank assigned to the job of preventing the dominoes toppling in insurance or derivatives. In these industries, firms that are fundamentally solid can become troubled simply because of the travails of other firms further down the chain.

Many people argue that derivatives reduce systemic problems, in that participants who can’t bear certain risks are able to transfer them to stronger hands. These people believe that derivatives act to stabilize the economy, facilitate trade, and eliminate bumps for individual participants.

On a micro level, what they say is often true. I believe, however, that the macro picture is dangerous and getting more so. Large amounts of risk, particularly credit risk, have become concentrated in the hands of relatively few derivatives dealers, who in addition trade extensively with one other. The troubles of one could quickly infect the others.

On top of that, these dealers are owed huge amounts by non-dealer counter-parties. Some of these counter-parties, are linked in ways that could cause them to run into a problem because of a single event, such as the implosion of the telecom industry. Linkage, when it suddenly surfaces, can trigger serious systemic problems.

Indeed, in 1998, the leveraged and derivatives-heavy activities of a single hedge fund, Long-Term Capital Management, caused the Federal Reserve anxieties so severe that it hastily orchestrated a rescue effort. In later Congressional testimony, Fed officials acknowledged that, had they not intervened, the outstanding trades of LTCM – a firm unknown to the general public and employing only a few hundred people – could well have posed a serious threat to the stability of American markets. In other words, the Fed acted because its leaders were fearful of what might have happened to other financial institutions had the LTCM domino toppled. And this affair, though it paralyzed many parts of the fixed-income market for weeks, was far from a worst-case scenario.

One of the derivatives instruments that LTCM used was total-return swaps, contracts that facilitate 100% leverage in various markets, including stocks. For example, Party A to a contract, usually a bank, puts up all of the money for the purchase of a stock while Party B, without putting up any capital, agrees that at a future date it will receive any gain or pay any loss that the bank realizes.

Total-return swaps of this type make a joke of margin requirements. Beyond that, other types of derivatives severely curtail the ability of regulators to curb leverage and generally get their arms around the risk profiles of banks, insurers and other financial institutions. Similarly, even experienced investors and analysts encounter major problems in analyzing the financial condition of firms that are heavily involved with derivatives contracts.

The derivatives genie is now well out of the bottle, and these instruments will almost certainly multiply in variety and number until some event makes their toxicity clear. Central banks and governments have so far found no effective way to control, or even monitor, the risks posed by these contracts. In my view, derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal.
 

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