18,018 research outputs found
On Pricing of Discrete Asian and Lookback Options under the Heston Model
We propose a new, data-driven approach for efficient pricing of - fixed- and
float-strike - discrete arithmetic Asian and Lookback options when the
underlying process is driven by the Heston model dynamics. The method proposed
in this article constitutes an extension of our previous work, where the
problem of sampling from time-integrated stochastic bridges was addressed. The
model relies on the Seven-League scheme, where artificial neural networks are
employed to "learn" the distribution of the random variable of interest
utilizing stochastic collocation points. The method results in a robust
procedure for Monte Carlo pricing. Furthermore, semi-analytic formulae for
option pricing are provided in a simplified, yet general, framework. The model
guarantees high accuracy and a reduction of the computational time up to
thousands of times compared to classical Monte Carlo pricing schemes
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
On Pricing of Discrete Asian and Lookback Options under the Heston Model
We propose a new, data-driven approach for efficient pricing of - fixed- and float-strike - discrete arithmetic Asian and Lookback options when the underlying process is driven by the Heston model dynamics. The method proposed in this article constitutes an extension of our previous work, where the problem of sampling from time-integrated stochastic bridges was addressed. The model relies on the Seven-League scheme, where artificial neural networks are employed to "learn" the distribution of the random variable of interest utilizing stochastic collocation points. The method results in a robust procedure for Monte Carlo pricing. Furthermore, semi-analytic formulae for option pricing are provided in a simplified, yet general, framework. The model guarantees high accuracy and a reduction of the computational time up to thousands of times compared to classical Monte Carlo pricing schemes
Tradable Schemes
In this article we present a new approach to the numerical valuation of
derivative securities. The method is based on our previous work where we
formulated the theory of pricing in terms of tradables. The basic idea is to
fit a finite difference scheme to exact solutions of the pricing PDE. This can
be done in a very elegant way, due to the fact that in our tradable based
formulation there appear no drift terms in the PDE. We construct a mixed scheme
based on this idea and apply it to price various types of arithmetic Asian
options, as well as plain vanilla options (both european and american style) on
stocks paying known cash dividends. We find prices which are accurate to in about 10ms on a Pentium 233MHz computer and to in a
second. The scheme can also be used for market conform pricing, by fitting it
to observed option prices.Comment: 13 pages, 5 tables, LaTeX 2
Efficient pricing of discrete arithmetic Asian options under mean reversion and jumps based on Fourier-cosine expansions
We propose an efficient pricing method for arithmetic Asian options based on Fourier-cosine expansions. In particular, we allow for mean reversion and jumps in the underlying price dynamics. There is an extensive body of empirical evidence in the current literature that points to the existence and prominence of such anomalies in the prices of certain asset classes, such as commodities. Our efficient pricing method is derived for the discretely monitored versions of the European-style arithmetic Asian options. The analytical solutions obtained from our Fourier-cosine expansions are compared to the benchmark fast Fourier transform based pricing for the examination of its accuracy and computational efficienc
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