The Concepts and Practice of Mathematical Finance

Introductory financial engineering is the most over-published topic in finance. Here's another one. In the tradition of Baxter and Rennie (1996) and Neftci (2000), Joshi delivers an intuitive introduction to some fairly sophisticated financial engineering. Like those other books, it targets readers who lack the background or inclination to learn stochastic calculus but want familiarity with the terminology and methodologies of financial engineering. This book won't make you a financial engineer, but it will help you to communicate with financial engineers.

 

Like Baxter and Rennie (1996) and Neftci (2000), Joshi delivers an informal introduction to concepts of stochastic calculus before proceeding to financial engineering. It differs from those other books in its emphasis on more practical applications. Both Baxter and Rennie and Neftci focus more on exploring advanced mathematical concepts or the theory underlying financial engineering. Joshi touches on such material on more of an as-needed basis. For this reason, Joshi can be a nice complement for either of those other books.

About half the book is dedicated to practical discussions of the pricing of exotics, interest rate derivatives, stochastic volatility and smile dynamics. Of course, "practical" is a relative term. This is a high-level treatment that doesn't delve into the nitty-gritty of implementing a pricing model. Indeed, lots of basic concepts receive only passing treatments as the book rushes towards more advanced discussions. Basic topics such as interest rates and compounding methods are explained in an ad hoc, as-needed manner. Indeed, at the start of the chapter on interest rate option pricing, the author advises that you forget everything he has already told you about continuously compounded interest rates.

Contents

1. Risk

2. Pricing methodologies and arbitrage

3. Trees and option pricing

4. Practicalities

5. The Ito calculus

6. Risk neutrality and martingale measures

7. The practical pricing of a European option

8. Continuous barrier options

9. Multi-look exotic options

10. Static replication

11. Multiple sources of risk

12. Options with early exercise features

13. Interest rate derivatives

14. The pricing of exotic interest rate derivatives

15. Incomplete markets and jump-diffusion processes

16. Stochastic volatility

17. Variance Gamma model

18. Smile dynamics and the pricing of exotic option

App. A. Financial and mathematical jargon

App. B. Computer project

App. C. Elements of probability theory

App. D. Hints and answers to exercises

A lot of finance also gets trampled. The author illustrates diversification with a two asset example that would be better described as hedging. He confuses systematic risk and systemic risk. He skips over pricing simple instruments, so he can start out with put and call options.

A positive aspect of the book is that it does illustrate plenty of practical financial engineering in a manner that will appeal to readers with a firm understanding of calculus and probability and passing familiarity with more advanced math and basic financial engineering. Anyone who has read Hull (2005)will be more than ready for this book.

Generally, I don't care for watered down books like this—what might be termed the "Cliff Notes" of financial engineering. That being said, they tend to be popular. This is especially true of Neftci (2000). I think, for a similar audience, this book could also be very popular.

For related books, see sections:

Markets - Derivatives

Financial Engineering - Basic Theory

Financial Engineering - Numerical Methods

Mathematics - Stochastic Calculus

 

 

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