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Consider a stock (XYZ Corporation) currently trading at $48, with volatility of 75%. The continuously compounded interest rate is 4%. The stock does not pay dividends. Fill in the following table of data for 1 year options on XYZ (based on the Black-Scholes Model, representing options on 1 share of stock). Indicate what source you used for the data, so that I can double check if something looks funny:How do you expect XYZ stock price movements to be correlated with ABC's business prospects? Explain why.Discuss ways ABC can hedge its risk using instruments tied to XYZ, given your assumption about how XYZ stock price movements are correlated with ABC's business prospects. Specifically, how can ABC hedge using an XYZ call? An XYZ put? An XYZ forward? XYZ stock? In each case, discuss how ABC would use that instrument ALONE---not in combination with other derivatives. The CEO of ABC has heard about spread positions and wants to use one. Would you recommend a bull spread or a bear spread on XYZ stock? Based on your recommendation in (c), construct a spread of that type using the options from (a). Graph the profit in 1 year as a function of the price of XYZ in one year. Be sure to label the maximum profit, the minimum profit, and the breakeven point(s).Does this strategy fully solve ABC's risk management problem? Explain why or why not.

XYZ Power Corporation owns a coal-fired power plant and generates power using coal. XYZ pays $500 in expenses not related to coal. The price that it pays for its coal input depends on market conditions, and XYZ buys a year's supply of coal once a year. Every two years, XYZ's regulator sets the price for power. It just established fixed rate of $1000 for the power XYZ generates. The risk manager is trying to avoid losses. Suppose the market price of coal is $400 and XYZ has just bought its supply, so has guaranteed a profit of -500-400 this year. Suppose the interest rate is 5% and there is a fair forward market. Can XYZ guarantee a profit next year? If yes, what will the profit be?Would you advise XYZ to buy a four year forward contract on coal? Would this guarantee a profit four years from now? Why or why not? Could a 4-year call or put help instead?Suppose there are no coal derivatives. But there are natural gas derivatives. Could these be used to help XYZ? Why or why not?

1. Consider a stock (XYZ Corporation) currently trading at $48, with volatility of 75%. The continuously compounded interest rate is 4%. The stock does not pay dividends. a) Fill in the following table of data for 1 year options on XYZ (based on the Black-Scholes Model, representing options on 1 share of stock). Indicate what source you used for the data, so that I can double check if something looks funny: Contract Call Put Call Put Call Put Call Put Strike 45 45 50 50 55 55 60 60 Price Dengue and Chikungunya are tropical diseases carried by Aedes mosquitoes. XYZ Corporation is developing a vaccine for Dengue. ABC Corporation is developing a drug to treat people who are infected with Chikungunya and will need to raise equity in one year to continue research and development. ABC management is nervous about the terms on which they will be able to raise equity and is considering hedges based on XYZ corporation stock. b. How do you expect XYZ stock price movements to be correlated with ABC's business prospects? Explain why. c. Discuss ways ABC can hedge its risk using instruments tied to XYZ, given your assumption about how XYZ stock price movements are correlated with ABC's business prospects. Specifically, how can ABC hedge using an XYZ call? An XYZ put? An XYZ forward? XYZ stock? In each case, discuss how ABC would use that instrument ALONE---not in combination with other derivatives. d. The CEO of ABC has heard about spread positions and wants to use one. Would you recommend a bull spread or a bear spread on XYZ stock? e. Based on your recommendation in (c), construct a spread of that type using the options from (a). Graph the profit in 1 year as a function of the price of XYZ in one year. Be sure to label the maximum profit, the minimum profit, and the breakeven point(s). f. Does this strategy fully solve ABC's risk management problem? Explain why or why not. 2. XYZ Power Corporation owns a coal-fired power plant and generates power using coal. XYZ pays $500 in expenses not related to coal. The price that it pays for its coal input depends on market conditions, and XYZ buys a year's supply of coal once a year. Every two years, XYZ's regulator sets the price for power. It just established fixed rate of $1000 for the power XYZ generates. The risk manager is trying to avoid losses. Suppose the market price of coal is $400 and XYZ has just bought its supply, so has guaranteed a profit of 100=1000-500-400 this year. Suppose the interest rate is 5% and there is a fair forward market. a) Can XYZ guarantee a profit next year? If yes, what will the profit be? b) Would you advise XYZ to buy a four year forward contract on coal? Would this guarantee a profit four years from now? Why or why not? Could a 4-year call or put help instead? c) Suppose there are no coal derivatives. But there are natural gas derivatives. Could these be used to help XYZ? Why or why not