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10. The current price of a non-dividend-paying stock is 39.6. Over the next year it is expected to rise to 43.7 or fall to 36.6. An investor buys put options with a strike price of 40.8. What is the value of each option? The risk-free interest rate is 0% per annum with continuous compounding. If the volatility of a non-dividend-paying stock is 21.8% per annum and a risk-free rate is 3.7% per annum, what is the Cox, Ross, Rubinstein parameter p for a tree with a three-month time step? On March 1 the price of a commodity is 1016 and the December futures price is 1013.7. On November 1 the price is 965 and the December futures price is 956.1. A producer of the commodity entered into a December futures contracts on March 1 to hedge the sale of the commodity on November 1. It closed out its position on November 1. What is the effective price (after taking account of hedging) received by the company for the commodity? A company will buy 1000 units of a certain commodity in one year. It decides to hedge 41% of its exposure using futures contracts. The spot price and the futures price are currently 99.1 and 94.6, respectively. If the spot price and the futures price in one year turn out to be 114.9 and 114.0, respectively. What is the average price paid for the commodity? The price of a stock on July 1 is 59.7. A trader buys 95 call options on the stock with a strike price of 59.4 when the option price is 2.1. The options are exercised when the stock price is 69.6. The trader's net profit is (ignoring discounting) An investor shorts 100 shares when the share price is 63.5 and closes out the position six months later when the share price is 41.7. The shares pay a dividend of 2.5 per share during the six months. What is the investor's net profit? The current price of a non-dividend paying stock is 29.7. Use a two-step tree to value a European put option on the stock with a strike price of 32.0 that expires in 6 months with u = 1.26 and d = 0.86. Each step is 3 months, the risk free rate is 7.7%. Six-month call options with strike prices of 33.9 and 43.5 cost 6.0 and 2.5, respectively. What is the maximum gain when a bull spread is created by trading a total of 200 options? An interest rate is 6.5% per annum with continuous compounding. What is the equivalent rate with semiannual compounding? (When writing your answer, please use decimals instead of the percentage sign. So if the answer is 4.7%, write it as 0.047.) A hedger takes a long position in a futures contract on a commodity on November 1, 2012 to hedge an exposure on March 1, 2013. The initial futures price is 60.7. On December 31, 2012 the futures price is 65.9. On March 1, 2013 it is 68.8. The contract is closed out on March 1, 2013. What gain is recognized in the accounting year January 1 to December 31, 2013? Each contract is on 1000 units of the commodity. The spot price of an investment asset is 34.7 and the risk-free rate for all maturities is 11.8% with continuous compounding. The asset provides an income of 1.0 at the end of the first year and at the end of the second year. What is the three-year forward price? 10. The current price of a non-dividend-paying stock is 39.6. Over the next year it is expected to rise to 43.7 or fall to 36.6. An investor buys put options with a strike price of 40.8. What is the value of each option? The risk-free interest rate is 0% per annum with continuous compounding. If the volatility of a non-dividend-paying stock is 21.8% per annum and a risk-free rate is 3.7% per annum, what is the Cox, Ross, Rubinstein parameter p for a tree with a three-month time step? On March 1 the price of a commodity is 1016 and the December futures price is 1013.7. On November 1 the price is 965 and the December futures price is 956.1. A producer of the commodity entered into a December futures contracts on March 1 to hedge the sale of the commodity on November 1. It closed out its position on November 1. What is the effective price (after taking account of hedging) received by the company for the commodity? A company will buy 1000 units of a certain commodity in one year. It decides to hedge 41% of its exposure using futures contracts. The spot price and the futures price are currently 99.1 and 94.6, respectively. If the spot price and the futures price in one year turn out to be 114.9 and 114.0, respectively. What is the average price paid for the commodity? The price of a stock on July 1 is 59.7. A trader buys 95 call options on the stock with a strike price of 59.4 when the option price is 2.1. The options are exercised when the stock price is 69.6. The trader's net profit is (ignoring discounting) An investor shorts 100 shares when the share price is 63.5 and closes out the position six months later when the share price is 41.7. The shares pay a dividend of 2.5 per share during the six months. What is the investor's net profit? The current price of a non-dividend paying stock is 29.7. Use a two-step tree to value a European put option on the stock with a strike price of 32.0 that expires in 6 months with u = 1.26 and d = 0.86. Each step is 3 months, the risk free rate is 7.7%. Six-month call options with strike prices of 33.9 and 43.5 cost 6.0 and 2.5, respectively. What is the maximum gain when a bull spread is created by trading a total of 200 options? An interest rate is 6.5% per annum with continuous compounding. What is the equivalent rate with semiannual compounding? (When writing your answer, please use decimals instead of the percentage sign. So if the answer is 4.7%, write it as 0.047.) A hedger takes a long position in a futures contract on a commodity on November 1, 2012 to hedge an exposure on March 1, 2013. The initial futures price is 60.7. On December 31, 2012 the futures price is 65.9. On March 1, 2013 it is 68.8. The contract is closed out on March 1, 2013. What gain is recognized in the accounting year January 1 to December 31, 2013? Each contract is on 1000 units of the commodity. The spot price of an investment asset is 34.7 and the risk-free rate for all maturities is 11.8% with continuous compounding. The asset provides an income of 1.0 at the end of the first year and at the end of the second year. What is the three-year forward price