You are the manager of the Bethela House Investment Fund. On 12 July, you receive notice that the fund will be sold on 30 August. The fund comprises a diversified portfolio of listed Australian shares. It is currently valued at $19 million. The current SPI200 index is 5415. Each point in SPI200 contract is worth $25. (a) You decided to hedge this risk using September SPI 200 futures. On 12 July, the contract price of the September SPI 200 futures contract was 5421. What would be the position you need to take to hedge against possible falls in the value of the portfolio? (b) On 30 August, the SPI200 index is 5000 and the futures contract was 5006. The value of the portfolio had fallen to $17 million. Evaluate the effectiveness of the hedge and the imperfection from the specification difference? (c) You decided to hedge this risk using September SPI 200 European option which has two months to maturity. The exercise price is 5415 and the risk-free interest rate is 1% per month. Furthermore, the SPI index is expected to either increase by 5% or decrease by 4.762% each month. The index does not pay dividends. Assume a risk-neutral world. Each index point is equal to $10. What is the value of the option? Show your calculations.

(d) If the SPI 200 option was an American option, then what is the value of the option?