14,566 research outputs found
Basket Options Valuation for a Local Volatility Jump-Diffusion Model with the Asymptotic Expansion Method
In this paper we discuss the basket options valuation for a jump-diffusion
model. The underlying asset prices follow some correlated local volatility
diffusion processes with systematic jumps. We derive a forward partial integral
differential equation (PIDE) for general stochastic processes and use the
asymptotic expansion method to approximate the conditional expectation of the
stochastic variance associated with the basket value process. The numerical
tests show that the suggested method is fast and accurate in comparison with
the Monte Carlo and other methods in most cases.Comment: 16 pages, 4 table
Momentum-Space Approach to Asymptotic Expansion for Stochastic Filtering
This paper develops an asymptotic expansion technique in momentum space for
stochastic filtering. It is shown that Fourier transformation combined with a
polynomial-function approximation of the nonlinear terms gives a closed
recursive system of ordinary differential equations (ODEs) for the relevant
conditional distribution. Thanks to the simplicity of the ODE system, higher
order calculation can be performed easily. Furthermore, solving ODEs
sequentially with small sub-periods with updated initial conditions makes it
possible to implement a substepping method for asymptotic expansion in a
numerically efficient way. This is found to improve the performance
significantly where otherwise the approximation fails badly. The method is
expected to provide a useful tool for more realistic financial modeling with
unobserved parameters, and also for problems involving nonlinear measure-valued
processes.Comment: revised version for publication in Ann Inst Stat Mat
Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach
In this work, we propose a new policy iteration algorithm for pricing
Bermudan options when the payoff process cannot be written as a function of a
lifted Markov process. Our approach is based on a modification of the
well-known Longstaff Schwartz algorithm, in which we basically replace the
standard least square regression by a Wiener chaos expansion. Not only does it
allow us to deal with a non Markovian setting, but it also breaks the
bottleneck induced by the least square regression as the coefficients of the
chaos expansion are given by scalar products on the L^2 space and can therefore
be approximated by independent Monte Carlo computations. This key feature
enables us to provide an embarrassingly parallel algorithm.Comment: The Journal of Computational Finance, Incisive Media, In pres
CVA and vulnerable options pricing by correlation expansions
We consider the problem of computing the Credit Value Adjustment ({CVA}) of a
European option in presence of the Wrong Way Risk ({WWR}) in a default
intensity setting. Namely we model the asset price evolution as solution to a
linear equation that might depend on different stochastic factors and we
provide an approximate evaluation of the option's price, by exploiting a
correlation expansion approach, introduced in \cite{AS}. We compare the
numerical performance of such a method with that recently proposed by Brigo et
al. (\cite{BR18}, \cite{BRH18}) in the case of a call option driven by a GBM
correlated with the CIR default intensity. We additionally report some
numerical evaluations obtained by other methods.Comment: 21 page
OPTION PRICING WITH V. G. MARTINGALE COMPONENTS
European call options are priced when the uncertainty driving the stock price follows the V. G. stochastic process (Madan and Seneta 1990). The incomplete markets equilibrium change of measure is approximated and identified using the log return mean, variance, and kurtosis. An exact equilibrium interpretation is also provided, allowing inference about relative risk aversion coefficients from option prices. Relative to Black-Scholes, V. G. option values are higher, particularly so for out of the money options with long maturity on stocks with high means. low variances, and high kurtosis.Option, pricing, Variance Gamma, martingale
Pricing Discrete Barrier Options under Stochastic Volatility
This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in pricing barrier options with discrete monitoring. To our knowledge, this paper is the first one that shows an analytical approximation for pricing discrete barrier options with stochastic volatility models. Furthermore, it provides numerical examples for pricing double barrier call options with discrete monitoring under Heston and ă-SABR models.
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