An Asian call option pays off max(Ave - K,0) at the maturity date where Ave is the

arithmetic average of the stock price over a given period of time.

We consider a three-step binomial tree to price a 1-year Asian call on Facebook where

the average is defined by

Ave = (Spot4m + Spot8m + Spot12m) / 3, where the Spot4m, Spot8m, Spot12m are market prices at end of 4 months, 8 months and 1 year respectively.

We assume that Facebook spot price is $140, its volatility is 10% and that Facebook is not expected to pay any dividend in the coming year. The strike price K is $115 and the risk-free interest rate is 7%.

(a) Calculate the tree parameters u, d, the growth factor a and the risk-neutral probability p. (Up, down movements need to match the volatility. Keep 4 decimal digits). (2 marks)

(b) What are the possible averages after 1 year? (2 marks)

(c) Price the Asian call using the 3-step binomial tree. Show all the details. (3 marks)

Cumulative Standard Normal function

N(x) for X>=0

For example: N(1.1693) = N(1.16) + 0.93 [N(1.17) - N(1.16)] = 0.8789

Rule: For x<0 ,N(x) = 1 - N(-x)