8,287 research outputs found
Sequential Monte Carlo pricing of American-style options under stochastic volatility models
We introduce a new method to price American-style options on underlying
investments governed by stochastic volatility (SV) models. The method does not
require the volatility process to be observed. Instead, it exploits the fact
that the optimal decision functions in the corresponding dynamic programming
problem can be expressed as functions of conditional distributions of
volatility, given observed data. By constructing statistics summarizing
information about these conditional distributions, one can obtain high quality
approximate solutions. Although the required conditional distributions are in
general intractable, they can be arbitrarily precisely approximated using
sequential Monte Carlo schemes. The drawback, as with many Monte Carlo schemes,
is potentially heavy computational demand. We present two variants of the
algorithm, one closely related to the well-known least-squares Monte Carlo
algorithm of Longstaff and Schwartz [The Review of Financial Studies 14 (2001)
113-147], and the other solving the same problem using a "brute force" gridding
approach. We estimate an illustrative SV model using Markov chain Monte Carlo
(MCMC) methods for three equities. We also demonstrate the use of our algorithm
by estimating the posterior distribution of the market price of volatility risk
for each of the three equities.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS286 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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
Two-state filtering for joint state-parameter estimation
This paper presents an approach for simultaneous estimation of the state and
unknown parameters in a sequential data assimilation framework. The state
augmentation technique, in which the state vector is augmented by the model
parameters, has been investigated in many previous studies and some success
with this technique has been reported in the case where model parameters are
additive. However, many geophysical or climate models contains non-additive
parameters such as those arising from physical parametrization of sub-grid
scale processes, in which case the state augmentation technique may become
ineffective since its inference about parameters from partially observed states
based on the cross covariance between states and parameters is inadequate if
states and parameters are not linearly correlated. In this paper, we propose a
two-stages filtering technique that runs particle filtering (PF) to estimate
parameters while updating the state estimate using Ensemble Kalman filter
(ENKF; these two "sub-filters" interact. The applicability of the proposed
method is demonstrated using the Lorenz-96 system, where the forcing is
parameterized and the amplitude and phase of the forcing are to be estimated
jointly with the states. The proposed method is shown to be capable of
estimating these model parameters with a high accuracy as well as reducing
uncertainty while the state augmentation technique fails
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