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Approximating stochastic volatility by recombinant trees


Akyildirim, Erdinc; Dolinsky, Yan; Soner, H Mete (2014). Approximating stochastic volatility by recombinant trees. Annals of Applied Probability, 24(5):2176-2205.

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.

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.

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13 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Scope:Discipline-based scholarship (basic research)
Language:English
Date:October 2014
Deposited On:31 Jan 2022 07:17
Last Modified:26 Jun 2024 01:51
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/13-AAP977
Official URL:https://doi.org/10.1214/13-AAP977
Other Identification Number:merlin-id:20846
  • Content: Published Version