Chapter 9
Numerical Methods for Option Pricing
Equation (8.26) provides a way to evaluate option prices. For some simple options,
such as the European call and put options, one can integrate (8.26) directly and obtain
a closed-form solution as in (8.18) o
Chapter 8
Black-Scholes Equations
1
The Black-Scholes Model
Up to now, we only consider hedgings that are done upfront. For example, if we write
a naked call (see Example 5.2), we are exposed to unlimited risk if the stock price rises
steeply. We can hedg
Chapter 10
Extensions of Black-Scholes Model
We have completed the Black-Scholes analysis of vanilla European call and put options in Chapter 8. Although the formulas presented are useful, there are many more
complicated situations in which the formulas a
Chapter 6
Geometric Brownian Motions
1
Normal Distributions
We begin by recalling the normal distribution briey. Let Z be a random variable
distributed as standard normal, i.e., Z N (0, 1). The probability density function of
Z is given by
2
1
(1)
pZ (z)
Chapter 7
Its Lemma
o
1
Its Lemma
o
Its lemma is the most important result (and tool) in doing stochastic analysis.
o
Roughly speaking, it relates the small change in a function of a random variable to
the small change in the random variable itself. In th
Chapter 5
Trading Strategies
1
Strategies Involving A Single Option and A Stock
One of the attractions of options is that they can be used to create a very wide range
of payo patterns. In the following we rst turn to several examples which involve a
singl
Chapter 1
Introduction
1
Acknowledgments
The rst seven chapters of this lecture notes were originally prepared by Prof. Xun Li of
the National University of Singapore (currently at Hong Kong Polytechnic University)
for the course Financial Mathematics I.
Chapter 2
Options
1
European Call Options
To consolidate our concept on European call options, let us consider how one can calculate the price of an option under very simple assumptions. Recall that the terminal
payo of a call option is c(T ) = max(S(T )
Chapter 4
Put-Call Parity
1
Bull and Bear
Financial analysts use words such as bull and bear to describe the trend in stock
markets. Generally speaking, a bull market is characterized by rising prices. Indeed,
an investor is sometimes called a bull when h
Chapter 3
Interest Rates and Forward
1
Interests and Present Values
When we put money in a bank, we earn interest. There are several types of interest.
First of all, there is the simple interest. Simple interest is when the interest you receive
is based o