1. (4 points) An Average Price call is a type of Asian option that pays off max{0, Savg K) at maturity (i.e., no early exercise is allowed) where Savg is the average of the stock prices from the start of the call to its maturity. For example, consider the following path for stock prices:

   Day Price 0 Start of option $100 1 $110 2 $121 3 $133.1

   In this case, the average stock price = (100 + 110 + 121 + 133.1)/4 = $116.025. [Note that although there are 4 days and 3 periods, the average is taken from the start date (i.e. over the 4 prices).]

   Consider an Average Price call with a maturity of 3 months (and can be exercised only at maturity), and an exercise price of $99. The underlying stock is currently traded at $100, while the risk-free rate is 5% p.a. Use a 3-period Binomial tree to price this call, given that you have determined that u = 1.1 and d = 0.9. Also, at time 0, what is the (risk-neutral) probability that this call will end up in the money? (Assume Continuous Compounding)