Question 1

Assume you are the risk manager of a hedge fund at Arcku Asset Management Plc, a UK based firm. The hedge fund is heavily invested in stocks and alternate investments due to its aggressive return targets. Strategic Investment targets and allocations are reviewed and revised by the Investment Committee on a quarterly basis on March 16^th, Jun 16^th, Sep 16^th and Dec 16^th. Hence, for the sake of simplicity, assume all derivative strategies have settlement/exercise date in line with these 4 dates or the nearest expiration dates available.

The equity portfolio is divided into 2 sub-portfolios: short-term and long-term capital gain targets. The Short to medium term return target sub-portfolio comprises mainly of value stocks. The managers pursue active trading based on style and benchmark deviations. As the main purpose of this portfolio is to provide liquidity and to meet short to medium term liabilities, trading is allowed as and when needed. On the other hand, the long-term return based strategic portfolio aims at significant capital gains to enhance the funds long-term net asset value, mostly comprising of growth stocks and physical assets. Strategic re-allocations are only allowed at quarter ends.

Mr. Peter Rogers, equity portfolio manager approaches you to consult on the use of Financial Derivatives using Options to hedge the equity portfolio. Mr. Peter Rogers has recently bought 20 million worth of Tesla stocks (10 m is allocated to long-term and 10m allocated to short-term sub-portfolio) based on the companys growth potential and current positive market outlook. However, he is aware that short term return expectations may not materialise and would like to hedge his position using covered calls and protective put.

In order to execute the 2 Option strategies for both types of stock sub-portfolios, you are considering 2 different methods of option valuation:

1. Year ended strategic re-adjustment using Calls and Puts on 10 m worth of Tesla stock in the Long-term portfolio, using 2 period Binomial Pricing model.

2. Use Black Scholes Mertin for short-term sub-portfolio.

You can choose exercises prices, expirations, risk free rate and measure of volatility to use as inputs in pricing the options.

Requirement:

1. Estimate the prices of European calls and puts for both strategies using the two-period binomial pricing model. Determine the hedge ratio, appropriate strategy and whether the strategy provided a perfect or imperfect hedge for each strategy. (15 marks)

2. How would the Call and Put prices differ if the options were American style.

(5 marks)

3. Estimate prices of European puts and calls for both strategies with two different expiration dates and two different exercise prices of your choice using the BSM model. (12 marks)

4. Do you agree with using Binomial pricing model for option pricing for stocks in long term return portfolio and BSM for short term? Hint: consider when trading is allowed. Also, discuss the main similarities and differences between these models and when should these be used? (8 marks)

Total: 40 marks