Black-Scholes and Beyond:
Option Pricing Models

 

Chriss is the definitive non-technical introduction to option pricing theory and financial engineering. While other elementary books may oversimplify to achieve accessible explanations, Chriss does not. He uses mathematics as necessary, but stops short of using any calculus. Also, he is careful to explain basic concepts such as exponentials or probability distributions. The result is an extraordinarily good book that achieves a high degree of sophistication with essentially no technical prerequisites.

 

The book opens with a chapter describing basic instruments: stocks, currencies, zero-coupon bonds, forwards, futures and options. Arbitrage relationships and basic pricing formulas are introduced. The next chapter covers essential mathematics, focusing especially on the normal distribution. A third chapter provides a non-technical introduction to Brownian motion and its use in financial modeling.

Two chapters develop the Black-Scholes framework for pricing options. These start with replicating portfolios and dynamic hedging and lead to an excellent non-technical introduction to the Black-Scholes differential equation and the role played by boundary conditions.

Contents

1. Stocks, Options, and Futures

2. Fundamental Mathematical Concepts

3. The Geometric Brownian Motion Model of Price Movements

4. The Black-Scholes Formula

5. More on the Black-Scholes Formula

6. Binomial Trees

7. Basic Option Pricing With Binomial Trees

8. The Volatility Smile

9. Implied Volatility Trees

10. Implied Binomial Trees

11. Pricing Barrier Options in the Presence of the Smile

The next step is risk neutral valuation, which leads to two practical chapters on pricing options with binomial trees. Three chapters cover volatility smiles, implied volatility trees and implied binomial trees. The book closes with a sophisticated chapter on pricing and hedging barrier options. Given the clarity and depth of this closing chapter, one is struck by how much Chriss has accomplished in such a non-technical book. It is masterful!

I highly recommend Chriss as either an alternative or supplement to standard, more technical introductions to financial engineering, such as Hull (2005). With more technical books, it is easy to get lost among the trees. Chriss shows you the forest.

 

 

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