Test for Derivatives: Options and Risk Management
Instructions:
(a) This is an 7-day take-home test. Answer the following THREE questions
(b) TWO hard copies of scripts attached to signed copies of the assignment submission form have to be placed in the assignment box in the lobby of the Carnegie Building by 3pm,17th Oct 18. Explain the results, diagrams and equations you use.
1. DundeeBest Corp is currently trading at 50. There are options with underlying DundeeBest will expire in 50 days. The three-month Treasury bill is currently with 5 percent annual rate for the same period.
DundeeBest is not expected to issue dividends.
(a) Show the payoffs diagrams at expiry for calls and puts for DundeeBest if exercise price of both options is 55. Explain the diagrams. What would the payoffs diagrams change if exercise price is 45 and the three-month Treasury bill trading with 10 percent annual rate for the same period instead?
(b) You are at the Exchanges and notice that European calls and puts for DundeeBest with exercise price of £55 is selling at £0.7 pounds and £6 respectively. Can you detect any mispricing of the European options? Demonstrate how an arbitrage transaction is executed. Explain your strategy in details and show why the arbitrage opportunities would only disappear in a short period of time.
(c) You are at the Exchanges and notice that a European call of DundeeBest with exercise price 58 is selling for £0.29 and a European call of DundeeBest with exercise price 46 is selling for £4.94, all expired in 50 days.
You decide to construct a portfolio with the strategy: Buy 1 call with exercise price of 46 and sell 1 call with exercise price of 58. Show the payoff and profit of the portfolio at the maturity date (explain the diagram according to exercise prices ranges.) If you are a speculator, explain the market outlook you might have for constructing such a portfolio.
2. A stock XYZ is currently trading at £100 and can either go up 20 percent or go down 20 percent six months later. The risk-free rate from Treasury Bills are currently trading with 4 percent returns per year.
Assume that exercise price is £90.
(a) Show the price of a European call, expiring in 6 months. Explain every step of your computations. In your answers, please explain the hedge portfolio used to price the option, and how you can use the law of arbitrage to price the option.
(b) Show the price of a European call option, expiring in 12 months by a 2-step binomial tree method, with each step lasting 6 months. 15%
3. You work as a stock portfolio manager in the City of London currently in charge of a portfolio worth £70 million. The estimated risk for the portfolio is around 30% per year. Currently the risk-free rate is 2 percent per year.
Assume that the stocks in your portfolio pay no dividends. You expect that due to the Brexit risk, the downside risk of your portfolio would be higher in the next 6 months. You then sell 20 million of the portfolio and put it in riskfree asset such as Treasury Bills, with remaining stock portfolio worth £50 million now. You try to insure or hedge away potential (downside) risk of the remaining stock portfolio in 6 months.
You consult a dealer from an investment bank who can design a specific European put option for your portfolio of £50 million with exercise price of £53 million, expiring in 6 months.
(i) Scenario 1: Describe your insurance strategy with such a European put option. And in your answer, show the total net value diagram of your strategy on stock portfolio, put and T-bills. Note that you use T-bills to buy the put option.
(ii) Scenario 2: You would like to hedge away the risk of stock portfolio by a put delta hedging. Describe your strategy, and show the total values of your unit trust when stock portfolios are valued at £40m, £48m, and £56m in six months. Assume you only hedge once now and keep the hedge ratio fixed afterwards. Note that you use T-bills to buy the put options.