Question 1
MPF has indicated interest in international investments in equity securities and has requested VAM to consider the different equity markets. VAM has indicated that the risk of interenational investments can be hedged using different derivative contracts. These may include use of exchange-traded derivatives and over the counter (OTC) contracts. VAM has identified Chicago Board of Options Exchange (CBOE) and the CME Group for trading options and futures respectively for managing risk of MPF’s potential investment portfolio. However, the Intercontinental Exchange (ICE) also trades options and futures and is considered an alternative to both CBOE and CME.
Required:
Compare the MSCI US Index Futures contract on ICE against the S&P500 Futures on the CME as well as the equity options on Apple listed on CBOE against the equity options on BT Group Plc listed on ICE. (8 marks)
Analyse the main relevant features of futures and options that determine whether futures or options contracts will be used. (7 marks)
Evaluate and recommend which futures and options contracts listed on ICE, CME and CBOE markets should be used in the context of MPF’s proposed investment. (10 marks)
(Total 25 marks)
(Word limit 800)
Question 2
You have been tasked by your line manager to prepare supporting calculations in your report for a presentation to be made before MPF’s management. These calculations should essentially demonstrate derivative pricing using the No Arbitrage Principle. To do so, you choose to demonstrate the pricing of futures and options contracts using Apple’s stock. The line manager also wants to understand more about the challenges to BSM in the real world in pricing call and put options and any alternatives.
Required:
Estimate the fair price of an equity futures on Apple’ stock expiring in 6 months’ time using the cost of carry model. You are required to cover the following too:
provide (select and make assumptions) any missing inputs.
explain all the inputs in your pricing model and justify each.
compare the price from your cost of carry model against the actual price of the stock in the spot market at the day close to determine if it in contango or backwardation. (8 marks)
1). Estimate the prices of both Apple’s call and put options trading on CBOE using two and three period binomial option pricing models as well as the BSM model. You must cover the following:
provide (select and make assumptions) any missing inputs.
explain all the inputs in your pricing model and justify each.
evaluate whether the call and the put options are over or under-valued based on the price estimates from your calculations compared to their actual prices at the end of trading day on CBOE. (12 marks)
2). For the two period binomial model, demonstrate that the estimated price of the call is fair using the hedge portfolio calculations over the two period and adjusting the hedge ratio accordingly. (4 marks)
Estimate the value of the risk free bonds from the put-call parity using first the prices of calls and puts from the BSM model in 2 above and then the actual prices of calls and puts available from OPRA in Eikon for the same calls and puts. Discuss the factors that could explain the differences in pricing across the two put-call parity calculations. (6 marks)
Explain why the BSM may not hold in the real world. Identify and discuss the factors that challenge BSM in practice and if there are any alternatives to BSM. (10 marks)
(Total 40 marks)
(Word limit 1,200)
Question 3
Though VAM Investments has a general preference for exchange-traded derivatives, the management of MPF is interested in knowing more about the use of OTC derivatives particularly swaps for managing the risks of their proposed investments in UK equities. Your line manager requires your report to cover this too.
Required:
Given that the investment will be exposed to both equity market risk and currency risk, explain the mechanics of an equity swap and a currency swap. (10 marks)
Illustrate the pricing of hypothetical equity swap contract (receiving $ Fixed Rate derived from $ Libor rates and paying the returns on Apple’s stock) and a currency swap contract (paying $ Fixed Rate and receiving £ Floating Rate); assume for both contracts a notional value of $1,000,000 and payments made quarterly for one year. For currency swap, the £ notional value should be calculated based on the spot exchange rate on the day of your calculations. For any missing Libor term rates, assume that the term structure of interest rates is linear and upward sloping. Provide detail descriptions of each step and explain how the two contracts manage the risks involved. (12 marks)
Illustrate how the value of the equity swap contract changes one month after it is initiated. Provide details of your assumption. (8 marks)
