Derivatives and Risk Analytics question

Attach all the mathematical calculation process (include all questions), please do not calculate in code! 1. Consider a two-period binomial tree model for a non-dividend paying stock. Assume the current price So = 63, risk-free rate r = 3%, and volatility as 10%. a) Find the price of a European call on the stock with time to maturity T = 1, strike price K = 60, The European call price: $______ (Keep two decimal places) b) Find the price of an American put on the stock with time to maturity T = 1, strike price K = 60. The American put price: $______ (Keep two decimal places) c) If it’s a European put with time to maturity T = 1, strike price K = 60., would your result be the same with part b)? _______ (Enter “Yes” or “No”‘) 2. Using Black-Scholes Model, a) Determine a European call option on a ND stock when the price is $52, the strike price is $50, the risk-free rate is 12%, and the volatility is 30%, and the time to maturity is 3 months. Then, calculate its delta. The option price: $______ (Keep 2 decimal places) Delta: ________ (Keep 2 decimal places) b) Determine a European put option on a NDP stock when the stock price is $69, the strike price is $70, the risk-free rate Is 5%, the volatility is 35%, and the time to maturity is 6 months. Then calculate its delta. The option price: $ _______ (Keep 2 decimal places) Delta: ________ (Keep 2 decimal places) 3. 4. Which of the following must post margin? A. The seller and the buyer of an option B. The buyer of an option C. Neither the seller nor the buyer of an option D. The seller of an option 5. Which of the following is true for a call option on a non-dividend-paying stock when the stock’s price equals the strike price? A. It has a delta of 0.5 B. It has a delta greater than 0.5 C. It has a delta less than 0.5 D. Delta can be greater than or less than 0.5 6. Which of the following best describes the term “spot price”? A. The price for delivery at a future time B. The price for immediate delivery C. The price of an asset that has been damaged. D. The price of renting an asset 7. When the non-dividend paying stock price is $20, the strike price is $20, the riskfree rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the Following is the price of a European call option on the stock? A. 20N(0.1) -19.7N(0.2) B. 20N(0.2) -19.7N(0.1) C. 19.7N(0.1) -20N(0.2) D. 19.7N(0.2) -20N(0.1) 8. What does N(x) denote? A. The area under a normal distribution from zero to x B. The area under a normal distribution beyond x C. The area under a normal distribution up to x D. The area under the normal distribution between -x and x 9. The variance of a Wiener process in time t is: A. t squared B. t C. 0 D. square root of t 10. The price of a stock is $67. A trader sells 5 put option contracts on the stock with a strike price of $70 when the option price is $4. The options are exercised when the stock price is $69. What is the trader’s net profit or loss? A. Loss of $1,000 B. Loss of $1,500 C. Loss of $500 D. Gain of $1,500 11. What was the original Black-Scholes-Merton model designed to value? A. A European or American option on a stock providing no dividends B. A European option on a stock providing no dividends. C. A European option on any stock D. A European or American option on any stock 12. The process followed by a variable X is dX = mX dt + sX dz What is the coefficient of dz in the process for the square of X? A. msX B. sX^2 C. 2sX^2 D. sX 13. How can a straddle be created? A. Buy one call and one put with the same strike price and same expiration date B. Buy one call and one put with different strike prices and same expiration date C. Buy one call and two puts with the same strike price and expiration date D. Buy two calls and one put with the same strike price and expiration date 14. Who initiates delivery in a corn futures contract? A. The exchange B. Either party C. The party with the short position. D. The party with the long position 15. An investor sells a futures contract an asset when the futures price is $1,500. Each contract is on 100 units of the asset. The contract is closed out when the futures price is $1,540. Which of the following is true? A. The investor has made a loss of $2,000. B. The investor has made a gain of $4,000. C. The investor has made a gain of $2.000 D. The investor has made a loss of $4,000 16. What is a repo rate? A. Overnight rate B. The rate implicit in a transaction where securities are sold and bought back later at a higher price. C. A rate where the credit risk is relative high D. An uncollateralized rate 17. A variable × starts at zero and follows the generalized Wiener process dx = a dt + b dz where time is measured in years. During the first two years a = 3 and b = 4. During the following three years, a = 6 and b = 3. What is the expected value of the variable at the end of 5 years? A. 30 B. 16 C. 24 D. 20 18. Maintaining a delta-neutral portfolio is an example of which of the following? A. Static hedging B. Hedge and forget strategy C. Stop-loss strategy D. Dynamic hedging 19. Which of the following describes a covered call? A. A short call option on a stock plus a short position in the stock B. A long call option on a stock plus a short put option on the stock. C. A short call option on a stock plus a long position in the stock D. A long call option on a stock plus a long position in the stock 20. An interest rate is 6% per annum with annual compounding. What is the equivalent rate with continuous compounding? A. 6.17% B. 8.45% C. 5.83% D. 3.14% 21. When the stock price increases with all else remaining the same, which of the following is true? A. Both calls and puts decrease in value B. Puts increase in value while calls decrease in value C. Both calls and puts increase in value D. Calls increase in value while puts decrease in value 22. The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. What is the price of a one-year European put option on the stock with a strike price of $50? A. $6.00 B. $7.00 C. $2.09 D. $8.10 23. The current price of a non-dividend-paying stock is $40. Over the next year, it is expected to rise to $42 or fall to $37. An investor buys one-year put options with a strike price of $41. Which of the following is necessary to hedge the position? A. Buy 0.2 shares for each option purchased B. Buy 0.8 shares for each option purchased C. Sell 0.8 shares for each option purchased D. Sell 0.2 shares for each option purchased

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