# International Investment and Risk

2) Assume that on 1/8/2012, when the WBK share price was S= AUD 22.5 a trader has sold 200,000 European WBK call options with strike price K=25 and expiration date 1/11/2012. Suppose that the amount received for the options was AUD 200,000. Further assume that the yearly standard deviation of WBK returns is 40%, the risk-free rate is 3% and that WBK doesn’t pay any dividend during the time-period from 1/8/ 2012 to 1/11/2012. (20 Marks) a) Using the DerivaGem software, apply the Black-Scholes formula to calculate the price of the option as well as the delta, gamma, vega, theta and rho of the option (we can use week as the time units with respect to time to exercise and we assume there are 52 weeks in each year). Interpret your results. Further, provide a graph showing (i) the relationship between the value of the option and the strike price, (ii) the Delta of the option as a function of the stock price, (iii) the relationship between the Gamma of the option and the volatility of the stock price, (iv) the relationship between Vega of the option and the stock price, (v) the relationship between Rho of the option and the stock price. For each graph, provide a brief explanation and interpretation. b) Explain how the trader can hedge the risk and make his option portfolio delta neutral. Further assume that every week (on 1/8, 8/8, 15/8, 22/8 etc.) until maturity of the option, the trader decides to rebalance his portfolio to preserve delta neutrality. Provide a Table that contains for each week, the share price, the current delta of the option, the number of shares purchased/sold, the cost of shares purchased/sold, the cumulative cost including interest and the interest cost. What is the overall profit or loss of the trader at maturity of the option? Interpret your results. c) Assume that on 1/8/2012 there is another WBK call option available in the market with strike price K=AUD 23 and expiration date 27/9/2012. Assume again that the yearly standard deviation of WBK returns is 40% and the risk-free rate is 3%. Illustrate how on 1/8/2012 this option can be used to create (i) a delta- and gamma neutral portfolio; (ii) a delta- and vega-neutral portfolio.

3) Assume that the risk-free rates (treasury rates) are 3% for 6 months and 3.5%...

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