Approximating stochastic volatility by recombinant trees

Erdinç Akyildirim, Yan Dolinsky, H. Mete Soner

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processes and take values in a two-dimensional binomial tree. The other two components of the Markov process are the increments of random walks with simple values in {-1,+1}. The resulting efficient option pricing equations are numerically implemented for general American and European options including the standard put and calls, barrier, lookback and Asian-Type pay-offs. The weak and extended weak convergences are also proved.

Original languageEnglish (US)
Pages (from-to)2176-2205
Number of pages30
JournalAnnals of Applied Probability
Volume24
Issue number5
DOIs
StatePublished - Oct 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Heston model
  • Recombinant trees
  • Stochastic volatility
  • Weak convergence

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