Jupiter Investments

Jupiter Investments is a mid-size firm that specialises in investment management services to institutional investors in the pension fund industry. You have recently recruited as a Junior Analyst on the derivatives trading desk and have been assigned to look after Swan Pensions, one of Jupiters prime clients. Swans portfolio consists of investments in UK equities as well as US equities. Historically, Swan has mandated Jupiter to rely on portfolio diversification to manage the risk of its equity investments. However, recently it has realised that both the UK and US equity markets are highly co-integrated and increasingly move in tandem leaving its portfolio investments at higher risk. Swan is now considering the use of derivatives contracts to manage the risk of portfolio investments. As a starting point, it has requested your line manager at Jupiter to make a presentation before the investment committee of Swan Pensions. To help prepare for this presentation, your line manager has tasked you to write a report.

Question 2 1400 words

Your line manager wants to demonstrate the pricing of futures and options to the investment committee at Swan Pensions and requires you to prepare supporting calculations in your report for his presentation. 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 contract on BP listed on Eurex Exchange.

Required:

1. Estimate the fair price of any BP futures contract on Eurex using the cost of carry model. You are required to cover the following too:
   1. provide (select and make assumptions) any missing inputs.
   2. explain all the inputs in your pricing model and justify each.
   3. compare the price from your cost of carry model against the actual price at the day close and explain any underlying reasons for the under-pricing or over-pricing.
2. A). Estimate the prices of both a BP call and a BP put option trading on Eurex Exchange using two and three period binomial option pricing models as well as the BSM model. You must cover the following:
   1. provide (select and make assumptions) any missing inputs.
   2. explain all the inputs in your pricing model and justify each.
   3. 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 on Eurex Exchange.

B). 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.

3. Estimate the value of the risk free bonds from the put-call parity using the prices of calls and puts from the BSM model in 2 above. If the actual call is overpriced, demonstrate the required positions as per the put-call parity to exploit the mispricing.
4. Explain the different option Greeks and their role in option pricing and valuation. Also explain delta and gamma hedging with examples of each.