Financial Mathematics: Profit Calculation from Stock Trades and Options - Prof. John Diniu, Assignments of Mathematics

Download Financial Mathematics: Profit Calculation from Stock Trades and Options - Prof. John Diniu and more Assignments Mathematics in PDF only on Docsity! University of Connecticut Math 3615: Financial Mathematics Problems Fall 2009 Examples – Module 10 10/22/2009 In these examples, ignore the effect of brokerage commissions and bid-ask spreads. Assume all options are European style (i.e., can be exercised only on the expiration date). Also assume that no dividends are paid. 1. Suppose that Stock A is currently trading at 60 and the continuously compounded risk- free interest rate is 0.05. (a) Write a formula for the profit from buying Stock A today and selling it in 6 months (i.e., express profit as a function of S0.5, the stock’s price 6 months from now). (b) If a 6-month call option on Stock A with a strike price of 60 has a premium of 6, write a formula for the profit from writing a call option on one share of Stock A. (c) Now write an expression for the combined profit for an investor who executes both of the transactions described in (a) and (b). What is the investor’s profit if the price of Stock A at the end of 6 months is 63? (d) Is there a single security that could be purchased or sold to produce the same profit (for any possible price of Stock A at t = 6 months) as the combination of (a) and (b)? If so, what is the name of that security? 2. The following questions are based on the facts from Problem 1. (a) What would be the price of the security described in 1. (d) if it produces the same profit as the combination of (a) and (b)? (b) How would the payoff from the security in 1. (d) differ from the payoff from the combination of the stock and the call option? (c) What other security (and what amount of that security) could be combined with the security in 1. (d) to produce the exact same cash flows on every date as the combination of the stock and the call option?