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Elementary Introduction to Mathematical Finance

ISBN-10: 0521192536
ISBN-13: 9780521192538
Edition: 3rd 2011 (Revised)
Authors: Sheldon M. Ross
List price: $120.00 Buy it from $60.94
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Book details

List price: $120.00
Edition: 3rd
Copyright year: 2011
Publisher: Cambridge University Press
Publication date: 2/28/2011
Binding: Hardcover
Pages: 322
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.232

Introduction and Preface
Probability
Probabilities and Events
Conditional Probability
Random Variables and Expected Values
Covariance and Correlation
Conditional Expectation
Exercises
Normal Random Variables
Continuous Random Variables
Normal Random Variables
Properties of Normal Random Variables
The Central Limit Theorem
Exercises
Brownian Motion and Geometric Brownian Motion
Brownian Motion
Brownian Motion as a Limit of Simpler Models
Geometric Brownian Motion
Geometric Brownian Motion as a Limit of Simpler Models
*The Maximum Variable
The Cameron-Martin Theorem
Exercises
Interest Rates and Present Value Analysis
Interest Rates
Present Value Analysis
Rate of Return
Continuously Varying Interest Rates
Exercises
Pricing Contracts via Arbitrage
An Example in Options Pricing
Other Examples of Pricing via Arbitrage
Exercises
The Arbitrage Theorem
The Arbitrage Theorem
The Multiperiod Binomial Model
Proof of the Arbitrage Theorem
Exercises
The Black-Scholes Formula
Introduction
The Black-Scholes Formula
Properties of the Black-Scholes Option Cost
The Delta Hedging Arbitrage Strategy
Some Derivations
The Black-Scholes Formula
The Partial Derivatives
European Put Options
Exercises
Additional Results on Options
Introduction
Call Options on Dividend-Paying Securities
The Dividend for Each Share of the Security Is Paid Continuously in Time at a Rate Equal to a Fixed Fraction f of the Price of the Security
For Each Share Owned, a Single Payment of fS(t<sub>d</sub>) Is Made at Time t<sub>d</sub>
For Each Share Owned, a Fixed Amount D Is to Be Paid at Time t<sub>d</sub>
Pricing American Put Options
Adding Jumps to Geometric Brownian Motion
When the Jump Distribution Is Lognormal
When the Jump Distribution Is General
Estimating the Volatility Parameter
Estimating a Population Mean and Variance
The Standard Estimator of Volatility
Using Opening and Closing Data
Using Opening, Closing, and High-Low Data
Some Comments
When the Option Cost Differs from the Black-Scholes Formula
When the Interest Rate Changes
Final Comments
Appendix
Exercises
Valuing by Expected Utility
Limitations of Arbitrage Pricing
Valuing Investments by Expected Utility
The Portfolio Selection Problem
Estimating Covariances
Value at Risk and Conditional Value at Risk
The Capital Assets Pricing Model
Rates of Return: Single-Period and Geometric Brownian Motion
Exercises
Stochastic Order Relations
First-Order Stochastic Dominance
Using Coupling to Show Stochastic Dominance
Likelihood Ratio Ordering
A Single-Period Investment Problem
Second-Order Dominance
Normal Random Variables
More on Second-Order Dominance
Exercises
Optimization Models
Introduction
A Deterministic Optimization Model
A General Solution Technique Based on Dynamic Programming
A Solution Technique for Concave Return Functions
The Knapsack Problem
Probabilistic Optimization Problems
A Gambling Model with Unknown Win Probabilities
An Investment Allocation Model
Exercises
Stochastic Dynamic Programming
The Stochastic Dynamic Programming Problem
Infinite Time Models
Optimal Stopping Problems
Exercises
Exotic Options
Introduction
Barrier Options
Asian and Lookback Options
Monte Carlo Simulation
Pricing Exotic Options by Simulation
More Efficient Simulation Estimators
Control and Antithetic Variables in the Simulation of Asian and Lookback Option Valuations
Combining Conditional Expectation and Importance Sampling in the Simulation of Barrier Option Valuations
Options with Nonlinear Payoffs
Pricing Approximations via Multiperiod Binomial Models
Continuous Time Approximations of Barrier and Lookback Options
Exercises
Beyond Geometric Brownian Motion Models
Introduction
Crude Oil Data
Models for the Crude Oil Data
Final Comments
Autoregressive Models and Mean Reversion
The Autoregressive Model
Valuing Options by Their Expected Return
Mean Reversion
Exercises
Index

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