answer these questions please, it is derivative securities module.

1. A trader buys 75 European put options with a strike price of $6.25 and a time to maturity of eight months. The price paid for each option is $1.10. The price of the underlying asset is $5.90 in eight months. What is the trader's gain or loss? 2. The three-year zero rate is 2% and the four-year zero rate is 1.75% (both continuously compounded). What is the forward rate for the fourth year? 3. An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are 5% and 7% (both expressed with continuous compounding). What is the six-month forward rate? 4. If the zero curve is flat at 2%, what is the price (to three significant digits) of a one year bond (face value $100 ) with 3% coupon rate, paid semi-annually? 5. Suppose that the standard deviation of monthly changes in the price of commodity A is $4. The standard deviation of monthly changes in a futures price for a contract on commodity B (which is similar to commodity A) is \$5. The correlation between the futures price and the commodity price is 0.5 . Commodity B futures contract specifies one futures contract is for 10,000 units of the commodity. What hedge ratio should be used when hedging a one month exposure to 5,000 units of commodity A? 6. You are given: (i) The current price of the stock is $90 (ii) The call option currently sells for $1.00 and the put option for $0.80 (iii) Both the call option and put option will expire in 5 years (iv) Both the call option and put option have a strike price of $100. Can you imply the continuously compounded risk-free interest rate (to two decimal places) that results in no arbitrage