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4. A financial institution just wrote 100 contracts of a European call option on a stock with a strike price $52. Each contract has 100

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4. A financial institution just wrote 100 contracts of a European call option on a stock with a strike price $52. Each contract has 100 shares of stock. This call's expiration is 4 weeks away, and its current price is $50. The stock price has an annual volatility 30%, and the annual risk-free interest rate is 6%. Using a simulation, the stock prices over the next few weeks are predicted as $51, $53, $52 and $54. (a) Using the Black-Scholes model with help from the MATLAB financial toolbox, compute values of the option and A, and thus complete the following table: Week to expiration Stock price Option value A value 4 50 (8 3 51 2 1 0 53 52 54 (b) Using the following table, set up a rebalancing strategy for a dynamical A-neutral portfolio by (12 adjusting the number of stock shares and the cumulative cost in each week. Week to Change in Number of Cost of Cumulative expiration A value shares bought shares cost 4 3 2 1 0 (c) Calculate the institution's net gain or loss at the maturity of the option. (4 4. A financial institution just wrote 100 contracts of a European call option on a stock with a strike price $52. Each contract has 100 shares of stock. This call's expiration is 4 weeks away, and its current price is $50. The stock price has an annual volatility 30%, and the annual risk-free interest rate is 6%. Using a simulation, the stock prices over the next few weeks are predicted as $51, $53, $52 and $54. (a) Using the Black-Scholes model with help from the MATLAB financial toolbox, compute values of the option and A, and thus complete the following table: Week to expiration Stock price Option value A value 4 50 (8 3 51 2 1 0 53 52 54 (b) Using the following table, set up a rebalancing strategy for a dynamical A-neutral portfolio by (12 adjusting the number of stock shares and the cumulative cost in each week. Week to Change in Number of Cost of Cumulative expiration A value shares bought shares cost 4 3 2 1 0 (c) Calculate the institution's net gain or loss at the maturity of the option. (4

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