a) If you exercise an American call at time t < T (where T is the expiration), do you exercise right before, or right after the stock pays its dividend at time t? Why?
b) Many companies (e.g., banks) practice what is called "yield curve arbitrage". The idea is that returns on longer-maturity debt are higher than for shorter maturity debt. An institution attempting to profit from this discrepancies will lend money long term while borrowing short term and rolling the short term debt, in order to profit from the difference. Is this an arbitrage?
c) Show that P(T2) is greater or equal than P(T1) for two American puts with maturities T2>T1. Show that it is NOT true for European puts.
e) The current price of a share of ABC, Inc. is $31 and the riskless rate of return is 10 percent per annum (annual compounding). Consider a European put and a European call sharing the common exercise price of $30 and the common maturity of 3 months. The price of the put is $2.25 and the price of the call is $2.35. Are there any arbitrage opportunities? If so, construct a trading strategy to take advantage of the opportunity.