73,718 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
Bayesian optimization for computationally extensive probability distributions
An efficient method for finding a better maximizer of computationally
extensive probability distributions is proposed on the basis of a Bayesian
optimization technique. A key idea of the proposed method is to use extreme
values of acquisition functions by Gaussian processes for the next training
phase, which should be located near a local maximum or a global maximum of the
probability distribution. Our Bayesian optimization technique is applied to the
posterior distribution in the effective physical model estimation, which is a
computationally extensive probability distribution. Even when the number of
sampling points on the posterior distributions is fixed to be small, the
Bayesian optimization provides a better maximizer of the posterior
distributions in comparison to those by the random search method, the steepest
descent method, or the Monte Carlo method. Furthermore, the Bayesian
optimization improves the results efficiently by combining the steepest descent
method and thus it is a powerful tool to search for a better maximizer of
computationally extensive probability distributions.Comment: 13 pages, 5 figure
A new rejection sampling method without using hat function
This paper proposes a new exact simulation method, which simulates a realisation from a proposal density and then uses exact simulation of a Langevin diffusion to check whether the proposal should be accepted or rejected. Comparing to the existing coupling from the past method, the new method does not require constructing fast coalescence Markov chains. Comparing to the existing rejection sampling method, the new method does not require the proposal density function to bound the target density function. The new method is much more efficient than existing methods for certain problems. An application on exact simulation of the posterior of finite mixture models is presented
- …