Books on Financial Mathematics

Books on Financial Mathematics

　　For General Reading
　　
　　Peter L. Bernstein
　　
　　Capital Ideas: The Improbable Origins of Modern Wall Street
　　
　　Free Press, 1992
　　
　　Every student who is interested in financial mathematics should read this
book. It explains the historical development of some important ideas in
economics related to financial mathematics.
　　
　　
　　
　　Peter L. Bernstein
　　
　　Against the Gods: The Remarkable Story of Risk
　　
　　John Wiley & Sons, 1996
　　
　　This is a sequel to Capital Ideas, and it is worth reading. It traces the
history of concept of probability in the point of view of risk.
　　
　　
　　
　　Emanuel Derman
　　
　　My Life as a Quant: Reflections on Physics and Finance
　　
　　John Wiley & Sons, 2004
　　
　　This is a personal history of financial mathematics.
　　
　　
　　
　　
　　
　　For Financial Mathematics
　　
　　- In the alphabetical order of author names -
　　
　　
　　
　　Martin Baxter and Andrew Rennie
　　
　　Financial Calculus: An Introduction to Derivative Pricing
　　
　　Cambridge University Press, 1996
　　
　　A concise introduction to option pricing based on martingale approach. This is
one of the early readable books that introduced martingale approach. No rigorous
mathematics is presented.
　　
　　
　　
　　Jamil Baz and George Chacko
　　
　　Financial Derivatives: Pricing, Applications, and Mathematics
　　
　　Cambridge University Press, 2004
　　
　　An introduction to financial mathematics for business majors, but it is also
useful for mathematics majors who want gain to some insight into how economists
use mathematics. The use of mathematics in the book relies more on intuition in
the beginning but in the last part of the book more rigorous mathematics is
introduced.
　　
　　
　　
　　Thomas Björk
　　
　　Arbitrage Theory in Continuous Time, 2nd ed.
　　
　　Oxford University Press, 2004
　　
　　An introduction to option theory based on martingale approach. Optimal
stochastic control is also presented.
　　
　　
　　
　　Z. Brzeźniak and T. Zastawniak
　　
　　Basic Stochastic Processes
　　
　　Springer, 1998
　　
　　A student trying to understand the Itô calculus should read this book. All the
exercise problems have solutions.
　　
　　
　　
　　Sasha Cyganowski, Peter Kloeden and Jerzy Ombach
　　
　　From Elementary Probability to Stochastic Differential Equations with MAPLE
　　
　　Springer, 2001
　　
　　If you are not good at programming or if you want to visualize data in
numerical simulations, this book may be helpful.
　　
　　
　　
　　Alison Etheridge
　　
　　A Course in Financial Calculus
　　
　　Cambridge University Press, 2002
　　
　　A concise introduction to option theory based on martingale approach.
　　
　　
　　
　　Hélyette Geman
　　
　　Commodities and Commodity Derivatives
　　
　　John Wiley & Sons, 2005
　　
　　A comprehensive and readable introduction to commodity market including
electricity.
　　
　　
　　
　　Desmond Highham
　　
　　An Introduction to Financial Option Valuation: Mathematics, Stochastics and
Computation
　　
　　Cambridge University Press, 2004
　　
　　An introduction to option pricing theory at undergraduate level with Monte
Carlo simulations in Matlab. It contains many anecdotes.
　　
　　
　　
　　John C. Hull
　　
　　Options, Futures, and Other Derivatives, 5th ed.
　　
　　Prentice Hall, 2002
　　
　　A general introduction to financial mathematics with minimum amount of
mathematics.
　　
　　
　　
　　Peter James
　　
　　Option Theory
　　
　　John Wiley & Sons, 2003
　　
　　A concise but thorough introduction to option theory including the numerical
method and martingale method. Practically oriented compared with other books,
but in the last part of the book rigorous and advanced mathematics is
introduced.
　　
　　
　　
　　Mark Joshi
　　
　　The Concepts and Practice of Mathematical Finance
　　
　　Cambridge University Press, 2003
　　
　　An introduction to financial mathematics including the numerical method and
martingale method. The book is more practically oriented compared with other
books.
　　
　　
　　
　　Marek Musiela and Marek Rutkowski
　　
　　Martingale Methods in Financial Modelling, 2nd ed.
　　
　　Springer, 2004
　　
　　A comprehensive and mathematically rigorous introduction to financial
mathematics based on martingale approach. For people with strong mathematical
background, this book is recommended.
　　
　　
　　
　　Salih N. Neftci
　　
　　Principles of Financial Engineering
　　
　　Academic Press, 2004
　　
　　An introduction to financial mathematics.
　　
　　
　　
　　Bernt Oksendal
　　
　　Stochastic Differential Equations: An Introduction with Applications, 6th ed.
　　
　　Springer, 2003
　　
　　This is a standard textbook on SDE at graduate level.
　　
　　
　　
　　Stanley R. Pliska
　　
　　Introduction to Mathematical Finance: Discrete Time Models
　　
　　Blackwell Publishers, 1997
　　
　　An introduction to financial mathematics using the discrete time models. There
are many concrete examples in the book.
　　

　
　　Paul Wilmott, Sam Howison and Jeff Dewynne
　　
　　The Mathematics of Financial Derivatives: A Student Introduction
　　
　　Cambridge University Press, 1995
　　
　　An introduction to financial mathematics in terms of numerical solution of the
Black-Scholes equation. It is advised to learn numerical analysis first before
starting to read this book.

其中，John Hull's "Options, Futures and other derivatives" 是textbook.
　　
　　Emanuel Derman's "Life as a Quant" mentions both the career and the human
sides of a quant。平时读来for fun。可能要有physics background的人读来会比较亲切，里面提到很多物理学的big
names,我自己是一直看到merton-black-scholes才有共鸣。
　　
　　另外用的一本是：
　　Jaksa Cvitanic and Fernando Zapatero (2004). Introduction to the Economics and
Mathematics of Financial Markets.
　　MIT Press, Cambridge Massachusetts.
　　里面 Options, futures and forward contracts, other derivative securities,
valuation, stochastic differential equations 什么都讲了一点，还包括
　　Ito's rule 和 martingale approach，是本不错的入门书。用的math比John Hull那本稍微深一点。
　　
　　另外有个问题：
　　Financial Mathematics里面常用的软件是什么?
　　学校里只教过S-plus 和 R，不过好像在统计方面用得比较多。

软件主要好象有C++，Excel，VBA等等。去国外大学网站查查就知道了。
一般用matlab比较多