求解三道关于期权定价的题

1.

Suppose a farmer is expecting that her crop of grapefruit will be ready for harvest and sale as 150, 000 pounds of grapefruit juice in 3 months time. She would like to use futures to hedge her risk but unfortunately there are no futures contracts on grapefruit juice. Instead she will use orange juice futures. Suppose each orange juice futures contract is for 15, 000 pounds of orange juice and the current futures price is F0 = 118.65 cents-per-pound. The volatility, i.e. the standard deviation, of the prices of orange juice and grape fruit juice is 20% and 25%, respectively, and the correlation coefficient is 0.7. What is the approximate number of contracts she should purchase to minimize the variance of her payoff?

2.

Consider a 1-period binomial model with R = 1.02, S0 = 100, u = 1/d = 1.05. Compute the value of a European call option on the stock with strike K = 102. The stock does not pay dividends.（answer rounded to two decimal places.)

3.

When you construct the replicating portfolio for the option in the previous question， how many dollars do you need to invest in the cash account. (answer rounded to three decimal places)