Problem 3: Consider an at-the-money American style call option (price today equals strike price) on a non-dividend paying stock with 1 year to maturity and a strike price of $100. Assume risk-free rate to be 0%. Construct a 2-period binomial model assuming the stock price can only move up by 20% and down by 30%

1. Show the binomial tree for the stock prices over the next year.
2. What are the possible call option payoffs in one years time?
3. What is the Delta of the call option in 6 months if the stock price goes up?
4. What is the risk-neutral probability of an up move?

-rxtz orxt: - Dxe -ooix 3 Problem 1 So= $163 ; r = 1 %; D = 10% of So at end of each yo, T= 3 yrs 1. F? So-D xerxt, _ Dr w/ ti=i = $163 - $16.3 x 6 0.01x $16.3xe For too xerxT for is lower than ton (theachical price), then buy for and sell synthetic foward; the wise do the opposite $16 3 1 - 2 2 3 If observed price -0.025%! - Problem 2 S. - $4,289;rl%; S = 2.5%; T=1 1. Fer=Soxe SXT = $4,289 x 2. For = Fo, fx e XT 3 See Problem I point 3 xe Problem 3 C=? for So= $100; K= $100; u = 1.2, d=0.7, 50% 7 2 Can = max( Suu K;o) N-27 -> h=/ Sxu Sun - Suxu= ? T Cu Su Cud - max max (Sud-K;O) 1.+2. S. Sud - Slu= Suxd= ? 4 Sd Sdd = Sdxd = ? dd - max (Suid-K;o) e ? 2 3. Au = ? 4.P