8. Pricing Outside the Standard Black and Scholes Model

  1. Stefano M. Iacus

Published Online: 16 FEB 2011

DOI: 10.1002/9781119990079.ch8

Option Pricing and Estimation of Financial Models with R

Option Pricing and Estimation of Financial Models with R

How to Cite

Iacus, S. M. (2011) Pricing Outside the Standard Black and Scholes Model, in Option Pricing and Estimation of Financial Models with R, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119990079.ch8

Author Information

  1. Department of Economics, Business and Statistics, University of Milan, Italy

Publication History

  1. Published Online: 16 FEB 2011
  2. Published Print: 25 MAR 2011

ISBN Information

Print ISBN: 9780470745847

Online ISBN: 9781119990079

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Keywords:

  • Fast Fourier Transform (FFT) method;
  • L′evy market model;
  • Markov switching regimes;
  • option pricing;
  • standard Black and Scholes model;
  • telegraph process

Summary

The standard Black and Scholes model relies on several assumptions which allow for explicit formulas and easy calculations in most cases. Unfortunately some of these hypotheses like the constant volatility, Gaussianity of the returns and the continuity of the paths of the geometric Brownian motion process are unlikely to hold for many observed prices. Indeed, prices often show jumps, changes in volatility and the distribution of returns is usually skewed and with high tails. Most of these stylized facts are indeed captured by L′evy processes. This chapter examines the problem of pricing under the assumption that the dynamic of financial prices includes some kind of jump process and/or non-Gaussian behaviour. It focuses on L′evy process, and summarizes under which conditions L′evy process can be transformed into martingale. The chapter discusses option pricing using Fast Fourier Transform (FFT) method, pricing under telegraph process, and stochastic differential equations with Markov switching regimes.

Controlled Vocabulary Terms

Markov models; telegraph process