Question 1. For $600,000, you sold to a customer an OTM european call option contract on 200,000 XYZ shares. The Black-Scholes value of the option contract is $480,000. Right after selling the contract for such a good price, you covered your position by buying 200,000 shares of the XYZ stock, in case the option contract matures in the money. Which of the following is false about your covered position? (a) You have made a profit of $120,000 regardless whether the option matures in or out of the money. (b) You are likely to make a profit if the option contract matures in the money. (c) The covered position ensures that you have the shares to deliver to the customer if the option matures in the money. (d) You can lose money in the position when the option matures out of the money. Question 2. Assume that markets are efficient and that there are no transaction costs. Which of the following statements is false about delta trading as a strategy to hedge the risk of a bank's short position in a call option contract on a stock? (a) If the delta hedger trades more frequently, the hedging cost of the strategy is more likely to be similar to the fair option value. (b) Over the time up to maturity, if the stock price fluctuates below the strike price all the time, the cost of the trading strategy is zero. (c) A trade by the delta hedger is larger if the change in delta is larger. (d) The hedger buys the stock when the stock price rises and sells the stock when the price drops. Question 3. The stock of Gamma Airlines never pays any dividend (unlike the stock of Delta Airlines, which declared its 23rd consecutive quarterly dividend recently in February). The volatility of the Gamma Airlines stock price is 20%, and the interest rate is 2%. Which of the following is false? (a) The delta of a 3-month at-the-money put on the Gamma Airlines stock is negative. (b) The delta of a 3-month at-the-money call on the Gamma Airlines stock is higher than 0.5. (c) The delta of a 3-month forward on the Gamma Airlines stock is exactly 1. (d) The delta of a 3-month futures on the Gamma Airlines stock is also exactly 1. Question 4. A six-month european 50-strike call option on XYZ stock currently has a delta of 5 and a gamma of 10. You are currently short in a six-month 50-strike european straddle on XYZ stock and long in certain amount of the stock to hedge your total delta to zero. If the stock price suddenly (meaning dt 0 so that you can ignore theta and time decay) moves down by 80 cents, the loss of your delta-hedged position in the straddle (a) is approximately 7.2 dollars. (b) cannot be determined without giving the information about the Greeks of the put option on the XYZ stock
