Chapter 13.
Binomial Trees
Binomial Trees
Binomial trees are useful tools for pricing options. Construct charts of possible movements of a
stock and price according to the movements.
We assume that the stock price is a random walk, i.e. at each time step
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1
Options, Futures, and Other Derivatives 8th Edition,
Copyright John C. Hull 2012
CHAPTER 4
INTEREST RATES
INTEREST RATES THIS CHAPTER
! a
component in the valuation of all derivatives
! need to understand how are they measured a
Figure 1: A single step of a binary random walk, with stock price S, option
price f and probabilities p0 and q 0 of going up (u) or down (d).
Pricing Options for the Random Walk with Discrete
Steps
Consider a single step in a random walk
S0 given at t = 0
1
Capital Asset Pricing Model (CAPM)
We now assume an idealized framework for an open market place, where all the risky assets
refer to (say) all the tradeable stocks available to all. In addition we have a risk-free asset (for
borrowing and/or lending in
Chapter 14
Stochastic Processes & Stock Options
1
Wiener Processes and It
os Lemma
More sophisticated approach to modeling the behavior of assets underlying derivatives - view
motion as a stochastic process.
A stochastic process is a process where future
Chapter 15:
The Black-Sholes-Merton
Model
1
The Stock Price Assumption
Consider a stock whose price is S
In a short period of time of length t, the
return on the stock is normally distributed:
S
t , 2 t
S
(
)
where is expected return and is
volatility