Title :
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
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;
Conference_Titel :
Decision and Control (CDC), 2010 49th IEEE Conference on
Conference_Location :
Atlanta, GA
Print_ISBN :
978-1-4244-7745-6
DOI :
10.1109/CDC.2010.5717667
