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Estimating option prices using multilevel particle filters

Department of Statistics and Applied Probability, National University of Singapore, 117546, Singapore

## Abstract    Full Text(HTML)    Figure/Table    Related pages

Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume follows a diffusion process. We consider the combination of two methodologies in this direction. The first is the well-known multilevel Monte Carlo (MLMC) method [7], which is known to reduce the computational effort to achieve a given level of mean square error (MSE) relative to MC in some cases. Sequential Monte Carlo (SMC) (or the particle filter (PF)) methods (e.g. [6]) have also been shown to be beneficial in many option pricing problems potentially reducing variances by large magnitudes (relative to MC) [11, 17]. We propose a multilevel particle filter (MLPF) as an alternative approach to price options. We show via numerical simulations that under suitable assumptions regarding the discretization of the SDE driven by Brownian motion the cost to obtain O$(\epsilon^2)$ MSE scales like O$(\epsilon^{-2.5})$ for our method, as compared with the standard particle filter O$(\epsilon^{-3})$.
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# References

1. Barndoff-Nielsen OE, Shephard N (2001) Non-Gaussian OU-based models and some of their uses in financial economics. J Roy Statist Soc B 63: 167–241.

2. Boyle PP (1977) Options: a Monte Carlo approach. J Fin Econ 4: 323–338.

3. Cerou F, Del Moral P, Guyader A (2011) A non-asymptotic theorem for unnormalized FeynmanKac particle models. Ann Inst Henri Poincaire 47: 629–649.

4. Del Moral P (2004) Feynman-Kac formulae: genealogical and interacting particle systems with applications, New York: Springer.

5. Del Moral P, Jasra A, Law KJH, et al. (2017) Multilevel Monte Carlo samplers for normalizing constants. ACM TOMACS 27: 20.

6. Doucet A, Johansen A (2011) A tutorial on particle filtering and smoothing: fifteen years later, In: Handbook of Nonlinear Filtering, Oxford: Oxford University Press.

7. Giles MB (2008) Multilevel Monte Carlo path simulation. Oper Res 56: 607–617.

8. Giles MB (2015 ) Multilevel Monte Carlo methods. Acta Numerica 24: 259–328.

9. Glasserman P (2013) Monte Carlo Methods in Financial Engineering, New York: Springer.

10. Glasserman P, Staum J (2001) Conditioning on one-step survival for barrier options. Oper Res 49: 923–937.

11. Jasra A, Del Moral P (2011) Sequential Monte Carlo methods for option pricing. Stoch Anal Appl 29: 292–316.

12. Jasra A, Stephens A, Doucet A, et al. (2011) Inference for Lévy-driven stochastic volatility models via adaptive sequential Monte Carlo. Scand J Statist 38: 1–22.

13. Jasra A, Doucet A (2009) Sequential Monte Carlo methods for di usion processes. Proc Roy Soc A 465: 3709–3727.

14. Jasra A, Kamatani K, Law KJH, et al. (2017) Multilevel particle filters. SIAM J Numer Anal 55: 3068–3096.

15. Jasra A, Kamatani K, Osei PP, et al. (2018) Multilevel particle filters: normalizing constant estimation. J Statist Comp 28: 47–60.

16. Sen D, Thiery A, Jasra A (2018) On coupling particle filter trajectories. J Statist Comp 28: 461–475.

17. Sen D, Jasra A, Zhou Y (2017) Some contributions to sequential Monte Carlo methods for option pricing. J Statist Comp Sim 87: 733–752.

18. Shevchenko P, Del Moral P (2016) Valuation of barrier options using sequential Monte Carlo. J Comp Fin 20: 1–29.