Stochastic volatility: Option pricing using a multinomial recombining tree

Ionut Florescu, Frederi G. Viens

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)151-181
Number of pages31
JournalApplied Mathematical Finance
Volume15
Issue number2
DOIs
StatePublished - Apr 2008

Keywords

  • Incomplete markets
  • Monte Carlo method
  • Option pricing
  • Options market
  • Particle method
  • Random tree
  • Stochastic filtering
  • Stochastic volatility

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