This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ion has (subtracting the ﬁrst
equation from the second):
25 = 100x ⇒ x =
1
Substituting in, we also get y = − 8 1
4 Binomial Stock Example I (continued) So we see we have the replicating portfolio:
1
4 150 × 50  1
8 × 100
100 = So we must have
C0 =
Jump to Method #2 1
1
× 100 − × 95 = $13.125
4
8 Jump to Method #3 25
0 Expressing the Timevalue of Money
We could state the discount rate in a few ways:
1 90 2 100
100 The annualized interest rate (with no compounding) is
11.11%
100 111.10
111.10 The price of a 1year zero coupon bond with face value $1 is
1/1.111 = 0.90
3 The continuously compounded rate is − log(.9) = 10.54%, so
that the price of a 1year zero coupon bond is e −.1054 = 0.90.
Hull uses the last method. For now, all we need is the price of the
zero coupon bond, so I use the ﬁrst method. Oneperiod Binomial Model
Assumptions:
Binomial price movement
Frictionless market (no cost for buying or selling)
Bd < 1 < Bu (Why do we need this?)
Notation:
S0 : initial stock price
S0 u : stock price if it goes up
S0 d : stock price if it goes down
B : present value of $1 in the future
If you don’t like B , use 1
1+r instead Basic Idea of Pricing: ﬁnd a replicating portfolio, and use the no
arbitrage argument Option Delta Deﬁnition
Number of shares needed to replicate one call option is called
hedge ratio or option del...
View
Full
Document
This document was uploaded on 10/28/2013.
 Spring '13

Click to edit the document details