Estimation and pricing under long-memory stochastic volatility

Alexandra Chronopoulou, Frederi G. Viens

Research output: Contribution to journalArticlepeer-review

Abstract

We treat the problem of option pricing under a stochastic volatility model that exhibits long-range dependence. We model the price process as a Geometric Brownian Motion with volatility evolving as a fractional Ornstein-Uhlenbeck process. We assume that the model has long-memory, thus the memory parameter H in the volatility is greater than 0.5. Although the price process evolves in continuous time, the reality is that observations can only be collected in discrete time. Using historical stock price information we adapt an interacting particle stochastic filtering algorithm to estimate the stochastic volatility empirical distribution. In order to deal with the pricing problem we construct a multinomial recombining tree using sampled values of the volatility from the stochastic volatility empirical measure. Moreover, we describe how to estimate the parameters of our model, including the long-memory parameter of the fractional Brownian motion that drives the volatility process using an implied method. Finally, we compute option prices on the S&P 500 index and we compare our estimated prices with the market option prices.

Original languageEnglish (US)
Pages (from-to)379-403
Number of pages25
JournalAnnals of Finance
Volume8
Issue number2-3
DOIs
StatePublished - May 2012
Externally publishedYes

Keywords

  • Estimation
  • Long memory
  • Multinomial tree
  • Option pricing
  • Particle filtering
  • Stochastic volatility

ASJC Scopus subject areas

  • General Economics, Econometrics and Finance
  • Finance

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