8,442 research outputs found
Approximating stochastic volatility by recombinant trees
A general method to construct recombinant tree approximations for stochastic
volatility models is developed and applied to the Heston model for stock price
dynamics. In this application, the resulting approximation is a four tuple
Markov process. The first two components are related to the stock and
volatility processes and take values in a two-dimensional binomial tree. The
other two components of the Markov process are the increments of random walks
with simple values in . The resulting efficient option pricing
equations are numerically implemented for general American and European options
including the standard put and calls, barrier, lookback and Asian-type
pay-offs. The weak and extended weak convergences are also proved.Comment: Published in at http://dx.doi.org/10.1214/13-AAP977 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Multilevel Monte Carlo methods for applications in finance
Since Giles introduced the multilevel Monte Carlo path simulation method
[18], there has been rapid development of the technique for a variety of
applications in computational finance. This paper surveys the progress so far,
highlights the key features in achieving a high rate of multilevel variance
convergence, and suggests directions for future research.Comment: arXiv admin note: text overlap with arXiv:1202.6283; and with
arXiv:1106.4730 by other author
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
Sensitivity analysis of the early exercise boundary for American style of Asian options
In this paper we analyze American style of floating strike Asian call options
belonging to the class of financial derivatives whose payoff diagram depends
not only on the underlying asset price but also on the path average of
underlying asset prices over some predetermined time interval. The mathematical
model for the option price leads to a free boundary problem for a parabolic
partial differential equation. Applying fixed domain transformation and
transformation of variables we develop an efficient numerical algorithm based
on a solution to a non-local parabolic partial differential equation for the
transformed variable representing the synthesized portfolio. For various types
of averaging methods we investigate the dependence of the early exercise
boundary on model parameters
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