Question

Consider a stock (XYZ Corporation) currently trading at $50, with annualized volatility of 65%. The continuously compounded annualized 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 Strike   Price

Call 45

Put   45

Call   50

Put   50

Call   55

Put   55

Call   60

Put   60

Suppose Nova virus is a tropical disease carried by Nova mosquitoes, bugs which are otherwise harmless. XYZ Corporation is developing an environmentally safe pesticide that kills Nova mosquitoes. ABC Corporation is developing a vaccine for Nova virus. 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.

Answer 1

A.

Contract	Strike	Price
Call	45	15.56
Put	45	8.79
Call	50	13.51
Put	50	11.55
Call	55	11.75
Put	55	14.58
Call	60	10.23
Put	60	17.87

Call Price has been calculated using Black-Scholes equation and then Put price has been calculated using put-call parity.

B. From the given context, it seems that there was no other way to deal with Nova virus so, earlier there was demand but no supply. Now both XYZ and ABC are developing the pesticide and vaccine respectively to meet the demands of the market so it is expected that stock price of both the companies will move in same (upward) direction.

In general, if it's just consumer demand, then it affects everyone in the parallel direction. Generally, companies in the same industry have the positive correlation. So XYZ stock price movements are expected to be positively correlated with ABC's business.

C. Since ABC's business is positively correlated with XYZ stock movement, so to hedge the risk for the long position in stock one can take short call, long put, short forward and short stock. The underlying principle in choosing the position in hedging instrument corresponding to long position in stock is that as the stock price decreases we should have increase in payoff from hedging instrument to compensate for falling price of stock.

D. If the CEO expects that the stock price will increase moderately then he should go for bull spread and if he expects the stock price to decrease then he should go for the bear spread. Since there is positive correlation he should take bull spread as the CEO would expect that his business prospect will increase.