IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 07: Risk Management
Xuedong He
Fall, 2013
1 / 40
Illustration
A nancial institution that has sold for $300,000 a European call
option on $100,000 shares of a non-dividend-paying stock. We
ass
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 04: OptionsBlack-Scholes-Merton Model
Xuedong He
Fall, 2013
1 / 62
Option Pricing: Hedging
C(4t, u4 )
C(4t, u2 )
C(4t, 1)
C(4t, d2 )
C(4t, d4 )
Suppose we sell one share of the option and wan
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 08: Term Structure of Interest Rates and
Interest Rate Derivatives
Xuedong He
Fall, 2013
1 / 24
Interest Rates in the Market
Three types of rates in the market
Treasury rates: return rates of
IEOR E4700: Introduction to Financial
Engineering
Bridging Theories and Practice: Model Calibration and
Numerical Calculation in B-S-M Model
Xuedong He
Fall, 2013
1 / 44
Estimation
Before we can apply the Black-Scholes formula to price
options, we need de
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Fall 2013
Some Notes on Matrices and Vectors
1
Matrices and Vectors
An n-by-m matrix A consists of nm entries aligned in n rows and m columns, i.e.,
a
a1,2
1,1
a
a2,2
2,1
.
.
.
A= .
.
.
an1
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 09: Martingales and General Theory
Xuedong He
Fall, 2013
1 / 32
A Simple Gamble Game
Consider the following game: each day, a fair coin is tossed. If
the toss is head, then the participator c
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 07: Risk Management
Xuedong He
Fall, 2013
1 / 40
Illustration
A nancial institution that has sold for $300,000 a European call
option on $100,000 shares of a non-dividend-paying stock. We
ass
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 09: Martingales and General Theory
Xuedong He
Fall, 2013
1 / 32
A Simple Gamble Game
Consider the following game: each day, a fair coin is tossed. If
the toss is head, then the participator c
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 06: American Options
Xuedong He
Fall, 2013
1 / 24
Early Exercise
American options can be exercised at any time before maturity
2 / 24
Early Exercise
American options can be exercised at any t
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 06: American Options
Xuedong He
Fall, 2013
1 / 24
Early Exercise
American options can be exercised at any time before maturity
Exchange-traded stock options are generally American rather
than
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 2: Mean-variance Analysis
Xuedong He
Fall 2013
1 / 64
Uncertainty
Cash ow analysis can be applied to investment decision
problems in which the cash ow steams are deterministic
However, in rea
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 03: OptionsBinomial Tree Model
Xuedong He
Fall, 2013
1 / 32
Options
An option is the right, but not the obligation, to buy (or sell)
an asset under specied terms. This asset is called underly
IEOR4700: Introduction to Financial Engineering
Lecture Notes 1: Cash Flow Analysis
Xuedong He
Fall, 2013
1 / 59
Interest Theory
Interest is the result of time value of money
If you deposit $100 in a bank that pays 2% interest per year,
then at the end of
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 03: OptionsBinomial Tree Model
Xuedong He
Fall, 2013
1 / 32
Options
An option is the right, but not the obligation, to buy (or sell)
an asset under specied terms. This asset is called underly
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 04: OptionsBlack-Scholes-Merton Model
Xuedong He
Fall, 2013
1 / 62
Option Pricing: Hedging
C(4t, u4 )
C(4t, u2 )
C(4t, 1)
C(4t, d2 )
C(4t, d4 )
Suppose we sell one share of the option and wan
IEOR4700: Introduction to Financial Engineering
Lecture Notes 1: Cash Flow Analysis
Xuedong He
Fall, 2013
1 / 59
Interest Theory
Interest is the result of time value of money
2 / 59
Interest Theory
Interest is the result of time value of money
If you depo
IEOR E4700: Introduction to Financial
Engineering
Bridging Theories and Practice: Model Calibration and
Numerical Calculation in B-S-M Model
Xuedong He
Fall, 2013
1 / 44
Estimation
Before we can apply the Black-Scholes formula to price
options, we need de
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 2: Mean-variance Analysis
Xuedong He
Fall 2013
1 / 64
Uncertainty
Cash ow analysis can be applied to investment decision
problems in which the cash ow steams are deterministic
2 / 64
Uncertai
IEOR E4700: Introduction to Financial
Engineering
Lecture Notes 08: Term Structure of Interest Rates and
Interest Rate Derivatives
Xuedong He
Fall, 2013
1 / 24
Interest Rates in the Market
Three types of rates in the market
2 / 24
Interest Rates in the Ma