American option valuation with particle filters. (English) Zbl 1252.91082
Carmona, René A. (ed.) et al., Numerical methods in finance. Selected papers based on the presentations at the workshop, Bordeaux, France, June 2010. Berlin: Springer (ISBN 978-3-642-25745-2/hbk; 978-3-642-25746-9/ebook). Springer Proceedings in Mathematics 12, 51-82 (2012).
Summary: A method to price American-style option contracts in a limited information framework is introduced. The pricing methodology is based on sequential Monte Carlo techniques, as presented in [A. Doucet, N. De Freitas and N. Gordon (eds.), Sequential Monte Carlo Methods in Practice. New York, NY: Springer (2001; Zbl 0967.00022)], and the least-squares Monte Carlo approach of F. A. Longstaff and E. S. Schwartz [“Valuing American options by simulation: a simple least-squares approach”, Rev. Financ. Stud. 14, No. 1, 113–147 (2001; doi:10.1093/rfs/14.1.113)]. We apply this methodology using a risk-neutralized version of the square-root mean-reverting model, as used for European option valuation by S. L. Heston [“A closed-form solution for options with stochastic volatility with applications to bond and currency options”, Rev. Financ. Stud. 6, No. 2, 327–343 (1993; doi:10.1093/rfs/6.2.327)]. We assume that volatility is a latent stochastic process, and we capture information about it using particle filter based “summary vectors”. These summaries are used in the exercise/hold decision at each time step in the option contract period. We also benchmark our pricing approximation against the full-state (observable volatility) result. Moreover, posterior inference, utilizing market-observed American put option prices on the NYSE Arca Oil Index, is made on the volatility risk premium, which we assume is a constant parameter. Comparisons on the volatility risk premium are also made in terms of time and observability effects, and statistically significant differences are reported.
For the entire collection see [Zbl 1238.91005].
For the entire collection see [Zbl 1238.91005].
MSC:
| 91G70 | Statistical methods; risk measures |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 62F15 | Bayesian inference |
| 62L15 | Optimal stopping in statistics |
Keywords:
American options; latent stochastic process; Monte Carlo; optimal stopping; optimization; particle filter; posterior inference; risk premium; volatilityCitations:
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