Please answer all questions. Must show work when answering questions.

Must show work! 1. A bank invests $13 million in a stock fund and $7 million in a bond fund. Use the following information. The volatility of the stock fund is 35% per annum. The volatility of the bond fund is 20% per annum. The correlation between the stock fund and the bond fund is -0.6. Assume that the VaR follows the normal distribution. Calculate 10 - day 97% VaR of the portfolio Calculate the diversification benefit. 2. Suppose that you buy 10 put option contracts (each contract covers 100 shares and so 10 contracts are a total of 1000 shares). To hedge your option position, you use the dynamic delta hedging strategy and rebalance every week. Use the following information. Week 1's N(d1) = 0.36; Week 2's N(d1) = 0.24; Where N(d1) is the cumulative distribution function for a standard normal distribution. How many additional shares should be bought or sold during Week 2? 3. Generally, for equity options, as the strike price increases the implied decreases. Explain this in terms of the firm's leverage. 4. Suppose that you purchase a European call option that has a strike of $85 and a maturity of 6 months. The underlying stock is currently selling at $82 and the standard deviation on its return is 30%. Assume that the risk - free rate is 4%. a) Find the intrinsic price of the call option using the Black - Scholes - Merton model. b) If this is a put option, what is its intrinsic price based on the Black - Scholes - Merton model. 5. Using the following European call options information: K = $60, S0 = $70, T = 7.5 months, r = 6%, = 12% Find the probability of an up movement (P) based on the risk - neutral valuation. Find the European call option price using the risk - neutral valuation. Suppose that you use the real - world interest rate for this call option contains some risk premium and it is estimated at 20% now. Assuming that the call option's price obtained from part (b) does not change, the others being held constant, find the probability of an up movement in the real - world valuation. 6. Pink Bell Ice Cream is considering a weather call option to protect its sales position against unexpectedly low temperature in May and June. Assume that the strike price is $300, the payment rate is $1,500 per degree day and the payment cap is $180,000. What measure should be used, cumulative HDD or cumulative CDD? If the number of cumulative degree days turns out to be 412, what is the company's payoff? If the number of cumulative degree days turns out to be 445, what is the company's payoff