Option pricing, model calibration, and prediction with a switchable market: A stochastic approximation algorithm

Author

Yin, G. ; Yu, J. ; Zhang, Q.

Author_Institution

Dept. of Math., Wayne State Univ., Detroit, MI, USA

fYear

2010

fDate

15-17 Dec. 2010

Firstpage

6997

Lastpage

7002

Abstract

This paper considers option pricing under a regime-switching model. The switching process takes two different modes, and the underlying stock price evolves in accordance with the two modes dictated by a continuous-time, 2-state Markov chain. At a given instance, the price follows either a model of geometric Brownian motion or mean-reversion model on its market mode. We build stochastic approximation algorithms for model calibration. Convergence and rate of convergence are provided. Option market data are used to predict future market mode.

Keywords

Brownian motion; Markov processes; approximation theory; geometry; share prices; stochastic processes; continuous time state Markov chain; geometric Brownian motion; mean reversion model; option market; option pricing; regime switching model; stochastic approximation algorithm; stock price; switchable market; switching process; Approximation algorithms; Convergence; Least squares approximation; Markov processes; Switches; Option pricing; convergence; market mode prediction; parameter estimation; rate of convergence; stochastic approximation;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2010 49th IEEE Conference on

Conference_Location

Atlanta, GA

ISSN

0743-1546

Print_ISBN

978-1-4244-7745-6

Type

conf

DOI

10.1109/CDC.2010.5717667

Filename

5717667