Econ 4751 HW 4 Due on Thursday, 12/3/2009 Option and option pricing theory 1. (5 0’) Suppose Zack is going to travel in Italy in three months, and he needs €1000 at that time. The current exchange rate is €1=$1. Assume we know that the exchange rate goes either up or down by 5% each month, even though we can’t predict which even will happen exactly. The risk free interest rate is 2% each month. Yeshiva sells Zack an option to exchange €1000 for $1000 in three month. A) Find out the risk-neutral probability or risk-neutral measure. B) Give the value of the obligation that Yeshiva takes in three months, at each event. C) Go backward, find out the value of the obligation at each node in the event tree. D) What’s the price of the option that Yeshiva should charge Zack? E) Calculate Yeshiva’s hedging strategy two month after he issued the option. F) Calculate Yeshiva’s hedging strategy one month after he issued the option. G)
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Probability theory, Mathematical finance, Zack, Event Tree