# UConn MATH 5621 - Final Examination (3 pages)

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## Final Examination

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## Final Examination

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Pages:
3
School:
University Of Connecticut
Course:
Math 5621 - Financial Mathematics II
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Math 5621 Financial Mathematics II Mathematics of Corporate Finance Fall 2010 Final Examination December 10 15 2010 This is a take home examination due back to me by 5 PM Wednesday December 15 in my department mail box under my o ce door or by email You may consult any written source including textbooks notes solution manuals websites or anything else written You may NOT consult with any other person which would result in your failing the course Be sure to put your name on all papers submitted Please show all of your work and give all reasoning and calculations associated with your answers give me a chance to give partial credit on an incorrect answser The seven questions will be equally weighted in the grading 1 Consider a put option with an exercise price of 50 expiring four years from today on an underlying asset whch pays no dividends has a market value of 40 today and a standard deviation of return equal to 0 40 Use a binomial model with N 8 steps and probabilities qu qd 12 at each step BE CAREFUL HERE do not just copy formulas from the textbook there will be no partial credit for use of formulas inappropriate to these instructions Use a risk free annual rate of return of 2 BE CAREFUL HERE an annual rate of return is not the same thing as a continuously compounded annual rate of return a force of interest a What would be wrong with using the formulas for u and d in the textbook b What is the value of the put option today if it is an American option c Why is this value greater than 10 which I could get for exercising right away d What is the earliest time it might possibly be best to exercise this American put option e At time t 1 if you are at the up down node of the tree will the value of the risk free bonds in the replicating portfolio for a put option after rebalancing the portfolio be larger for the American put option or for the corresponding European put option By how much f Why are the two values in e di erent 2 Suppose that the current price in the

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