EIN 3354: Engineering Economy
Fall 2022
Homework # 7: Binomial No-Arbitrage Pricing Model
This homework is due on Tuesday, November 29, 2022 at 12:30 pm.
file should be named "lastname-firstname-HW7".
The submitted
1. Consider six months European put option with a strike price of $100 on a stock
with current price $100. There are two time steps and in each time step the stock price
either moves up by 10% or moves down by 10%. Risk-free interest rate is r = 5% (on
3 months).
(a) Find the current option price.
(b) Compute the number of shares of stock which should be held by the replicating
portfolio at time 0 and 1 (after 3 months).
2. Consider the 3-period binomial model with S0 = 100, u = 2, d = 21 and r = 14 . Find
the current price and compute the number of shares of stock which should be held by
the replicating portfolio at time 0, 1 and 2 for:
(a) Lookback call option with a strike price of $100 that pays off (at time three)
V3 = max Sn − 100 .
0≤n≤3
+
(b) Lookback put option with a strike price of $100 that pays off (at time three)
V3 = 100 − min Sn
.
0≤n≤3
+
(c) Asian call option with a strike price of $100 whose payoff (at time three) is
1
Y3 − 100 ,
V3 =
4
+
where Y3 =
3
P
Sk is the sum of stock prices between time 0 and time 3.
k=0
1