2,177 research outputs found
Sequential Monte Carlo Methods for Option Pricing
In the following paper we provide a review and development of sequential
Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte
Carlo-based algorithms, that are designed to approximate expectations w.r.t a
sequence of related probability measures. These approaches have been used,
successfully, for a wide class of applications in engineering, statistics,
physics and operations research. SMC methods are highly suited to many option
pricing problems and sensitivity/Greek calculations due to the nature of the
sequential simulation. However, it is seldom the case that such ideas are
explicitly used in the option pricing literature. This article provides an
up-to date review of SMC methods, which are appropriate for option pricing. In
addition, it is illustrated how a number of existing approaches for option
pricing can be enhanced via SMC. Specifically, when pricing the arithmetic
Asian option w.r.t a complex stochastic volatility model, it is shown that SMC
methods provide additional strategies to improve estimation.Comment: 37 Pages, 2 Figure
Smoothing the payoff for efficient computation of Basket option prices
We consider the problem of pricing basket options in a multivariate Black
Scholes or Variance Gamma model. From a numerical point of view, pricing such
options corresponds to moderate and high dimensional numerical integration
problems with non-smooth integrands. Due to this lack of regularity, higher
order numerical integration techniques may not be directly available, requiring
the use of methods like Monte Carlo specifically designed to work for
non-regular problems. We propose to use the inherent smoothing property of the
density of the underlying in the above models to mollify the payoff function by
means of an exact conditional expectation. The resulting conditional
expectation is unbiased and yields a smooth integrand, which is amenable to the
efficient use of adaptive sparse grid cubature. Numerical examples indicate
that the high-order method may perform orders of magnitude faster compared to
Monte Carlo or Quasi Monte Carlo in dimensions up to 35
Conditional Quasi-Monte Carlo with Constrained Active Subspaces
Conditional Monte Carlo or pre-integration is a useful tool for reducing
variance and improving regularity of integrands when applying Monte Carlo and
quasi-Monte Carlo (QMC) methods. To choose the variable to pre-integrate with,
one need to consider both the variable importance and the tractability of the
conditional expectation. For integrals over a Gaussian distribution, one can
pre-integrate over any linear combination of variables. Liu and Owen (2022)
propose to choose the linear combination based on an active subspace
decomposition of the integrand. However, pre-integrating over such selected
direction might be intractable. In this work, we address this issue by finding
the active subspaces subject to the constraints such that pre-integration can
be easily carried out. The proposed method is applied to some examples in
derivative pricing under stochastic volatility models and is shown to
outperform previous methods
Smoothing the payoff for efficient computation of basket option prices
We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster compared to Monte Carlo or Quasi Monte Carlo in dimensions up to 25
Multilevel Particle Filters for L\'evy-driven stochastic differential equations
We develop algorithms for computing expectations of the laws of models
associated to stochastic differential equations (SDEs) driven by pure L\'evy
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 of the discretization of the underlying driving L\'evy proccess,
our proposed method achieves optimal convergence rates. The cost to obtain MSE
scales like for our method, as compared with
the standard particle filter
The History of the Quantitative Methods in Finance Conference Series. 1992-2007
This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.
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