Stochastic Volatility: Option Pricing using a Multinomial Recombining Tree

The problem of option pricing is treated using the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be mean-reverting. Assuming that only discrete past stock information is available, an interacting partic...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematical finance. 2008-04, Vol.15 (2), p.151-181
Main Authors: Florescu, Ionuţ, Viens, Frederi G.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Decision trees
Incomplete markets
Monte Carlo method
option pricing
options market
particle method
random tree
Securities prices
stochastic filtering
Stochastic models
stochastic volatility
Studies
Volatility
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The problem of option pricing is treated using the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be mean-reverting. Assuming that only discrete past stock information is available, an interacting particle stochastic filtering algorithm due to Del Moral et al. (Del Moral et al., 2001 ) is adapted to estimate the SV, and a quadrinomial tree is constructed which samples volatilities from the SV filter's empirical measure approximation at time 0. Proofs of convergence of the tree to continuous-time SV models are provided. Classical arbitrage-free option pricing is performed on the tree, and provides answers that are close to market prices of options on the SP500 or on blue-chip stocks. Results obtained here are compared with those from non-random volatility models, and from models which continue to estimate volatility after time 0. It is shown precisely how to calibrate the incomplete market, choosing a specific martingale measure, by using a benchmark option.
ISSN:1350-486X
1466-4313
DOI:10.1080/13504860701596745