Sequential Monte Carlo Methods for Option Pricing

Jasra, Ajay; Moral, Pierre Del

doi:10.1080/07362994.2011.548993

Cited by 24 publications

(24 citation statements)

References 67 publications

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“…In the examples considered below, the original Lévy process has no drift and Brownian motion components, that is Σ = b = 0. Due to the linear drift correction F l 0 in the compensated compound Poisson process, the random jump times are refined such that the time differences between successive jumps are bounded by the accuracy parameter h l associated with the Euler discretization approximation methods in (5) and (15)- (16). However, since F l 0 = 0 here, due to symmetry, this does not affect the rate, as described in Remark 4.1.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Multilevel particle filters for Lévy-driven stochastic differential equations

2018

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We develop algorithms for computing expectations with respect to the laws of models associated to stochastic differential equations (SDEs) driven by pure Lévy processes. We consider filtering such processes and well as pricing of path dependent options. We propose a multilevel particle filter (MLPF) to address the computational issues involved in solving these continuum problems. We show via numerical simulations and theoretical results that under suitable assumptions regarding the discretization of the underlying driving Lévy proccess, our proposed method achieves optimal convergence rates: the cost to obtain MSE O( 2 ) scales like O( −2 ) for our method, as compared with the standard particle filter O( −3 ).

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Section: Numerical Examplesmentioning

confidence: 99%

“…for S > 0 given. As seen in [16] the calculation of the barrier option is non-trivial, in the sense that even importance sampling may not work well. We consider the (time) discretized version…”

Section: Barrier Optionmentioning

confidence: 99%

Multilevel particle filters for Lévy-driven stochastic differential equations

2018

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“…They proposed to estimate the contour boundary positions using a set of particle filters, and obtained importance result through experiments. In addition, particle filters are also successfully applied to positioning and tracking [33,34], communication [35], signal processing [36,37], financial and economics [38,39,40], etc.…”

Section: Related Workmentioning

confidence: 99%

Particle Filter with Hybrid Proposal Distribution for Nonlinear State Estimation

Wang¹,

Lin²,

Zhang³

et al. 2011

JCP

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Particle filters have been widely used in solving nonlinear filtering problems. Proposal Distribution design is a key issue for these methods and has vital effect on simulation results.  Various proposal distributions have been proposed to improve the performance of particle filters, but practical situations have promoted the researchers to design better candidate for proposal distributions in order to gain better performance. This paper proposes a hybrid proposal distribution designed for particle filtering framework. The algorithm uses hybrid Kalman filter to generate the proposal distribution, which make efficient use of the latest observations and generate more closed approximation of the posterior probability density. The yielded algorithm is named as hybrid Kalman particle filter. In the experiments, we use a scalar estimation model and a real world application problem to evaluate the new algorithm. The experimental results show that the new algorithm outperforms other algorithms with different proposal distributions. In order to reduce the time consumption of the new algorithm, we propose an improvement strategy, namely partition-conquer strategy, in which the particles are partitioned into two parts, with one part drawn from the hybrid Kalman filter, another part from the transition prior. The validity of the strategy is verified through an experiment

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“…Johannes et al (2009) and Peters et al (2013) to name a few. The applications of SMC methods in option pricing has been started recently by the second author in the series of articles Carmona et al (2012); Del Moral et al ( , 2012a; Jasra & Del Moral (2011). However, these methods are not widely known among option pricing practitioners and option pricing literature.…”

Section: Introductionmentioning

confidence: 99%

Valuation of barrier options using sequential Monte Carlo

Shevchenko¹,

Moral²

2016

JCF

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Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method for pricing barrier options with continuous and discrete monitoring of the barrier condition. Under the SMC method, simulated asset values rejected due to barrier condition are re-sampled from asset samples that do not breach the barrier condition improving the efficiency of the option price estimator; while under the standard Monte Carlo many simulated asset paths can be rejected by the barrier condition making it harder to estimate option price accurately. We compare SMC with the standard Monte Carlo method and demonstrate that the extra effort to implement SMC when compared with the standard Monte Carlo is very little while improvement in price estimate can be significant. Both methods result in unbiased estimators for the price converging to the true value as 1{? M , where M is the number of simulations (asset paths). However, the variance of SMC estimator is smaller and does not grow with the number of time steps when compared to the standard Monte Carlo. In this paper we demonstrate that SMC can successfully be used for pricing barrier options. SMC can also be used for pricing other exotic options and also for cases with many underlying assets and additional stochastic factors such as stochastic volatility; we provide general formulas and references.

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Sequential Monte Carlo Methods for Option Pricing

Cited by 24 publications

References 67 publications

Multilevel particle filters for Lévy-driven stochastic differential equations

Multilevel particle filters for Lévy-driven stochastic differential equations

Particle Filter with Hybrid Proposal Distribution for Nonlinear State Estimation

Valuation of barrier options using sequential Monte Carlo

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