Stochastic Volatility: Option Pricing Using a Multinomial Recombining Tree

38 Pages Posted: 26 May 2012 Last revised: 23 Mar 2018

See all articles by Ionut Florescu

Ionut Florescu

Stevens Institute of Technology

Frederi Viens

Purdue University

Date Written: May 25, 2005

Abstract

We treat the problem of option pricing under the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be meanreverting. Assuming that only discrete past stock information is available, we adapt an interacting particle stochastic filtering algorithm due to Del Moral, Jacod and Protter (Del Moral et al., 2001) to estimate the SV, and construct a quadrinomial tree 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. We compare our results to non-random volatility models, and to models which continue to estimate volatility after time 0. We show precisely how to calibrate our incomplete market, choosing a specific martingale measure, by using a benchmark option.

Keywords: incomplete markets, Monte-Carlo method, options market, option pricing, particle method, random tree, stochastic filtering, stochastic volatility

JEL Classification: C2

Suggested Citation

Florescu, Ionut and Viens, Frederi, Stochastic Volatility: Option Pricing Using a Multinomial Recombining Tree (May 25, 2005). Applied Mathematical Finance, Vol. 15, No. 2, 2008. Available at SSRN: https://ssrn.com/abstract=2066876

Ionut Florescu (Contact Author)

Stevens Institute of Technology ( email )

Castle Point on the Hudson
Hoboken, NJ 07030
United States

Frederi Viens

Purdue University ( email )

610 Purdue Mall
West Lafayette, IN 47906
United States

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