3,759 research outputs found
Monte Carlo Greeks for financial products via approximative transition densities
In this paper we introduce efficient Monte Carlo estimators for the valuation
of high-dimensional derivatives and their sensitivities (''Greeks''). These
estimators are based on an analytical, usually approximative representation of
the underlying density. We study approximative densities obtained by the WKB
method. The results are applied in the context of a Libor market model.Comment: 24 page
Smoking Adjoints: fast evaluation of Greeks in Monte Carlo calculations
This paper presents an adjoint method to accelerate the calculation of Greeks by Monte Carlo simulation. The method calculates price sensitivities along each path; but in contrast to a forward pathwise calculation, it works backward recursively using adjoint variables. Along each path, the forward and adjoint implementations produce the same values, but the adjoint method rearranges the calculations to generate potential computational savings. The adjoint method outperforms a forward implementation in calculating the sensitivities of a small number of outputs to a large number of inputs. This applies, for example, in estimating the sensitivities of an interest rate derivatives book to multiple points along an initial forward curve or the sensitivities of an equity derivatives book to multiple points on a volatility surface. We illustrate the application of the method in the setting of the LIBOR market model. Numerical results confirm that the computational advantage of the adjoint method grows in proportion to the number of initial forward rates
Pricing Step Options under the CEV and other Solvable Diffusion Models
We consider a special family of occupation-time derivatives, namely
proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96
(1999)]. We develop new closed-form spectral expansions for pricing such
options under a class of nonlinear volatility diffusion processes which
includes the constant-elasticity-of-variance (CEV) model as an example. In
particular, we derive a general analytically exact expression for the resolvent
kernel (i.e. Green's function) of such processes with killing at an exponential
stopping time (independent of the process) of occupation above or below a fixed
level. Moreover, we succeed in Laplace inverting the resolvent kernel and
thereby derive newly closed-form spectral expansion formulae for the transition
probability density of such processes with killing. The spectral expansion
formulae are rapidly convergent and easy-to-implement as they are based simply
on knowledge of a pair of fundamental solutions for an underlying solvable
diffusion process. We apply the spectral expansion formulae to the pricing of
proportional step options for four specific families of solvable nonlinear
diffusion asset price models that include the CEV diffusion model and three
other multi-parameter state-dependent local volatility confluent hypergeometric
diffusion processes.Comment: 30 pages, 16 figures, submitted to IJTA
Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations
In this article we consider the problem of pricing and hedging
high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We
assume a Black-Scholes market with time-dependent volatilities and show how to
compute the deltas by the aid of the Malliavin Calculus, extending the
procedure employed by Montero and Kohatsu-Higa (2003). Efficient
path-generation algorithms, such as Linear Transformation and Principal
Component Analysis, exhibit a high computational cost in a market with
time-dependent volatilities. We present a new and fast Cholesky algorithm for
block matrices that makes the Linear Transformation even more convenient.
Moreover, we propose a new-path generation technique based on a Kronecker
Product Approximation. This construction returns the same accuracy of the
Linear Transformation used for the computation of the deltas and the prices in
the case of correlated asset returns while requiring a lower computational
time. All these techniques can be easily employed for stochastic volatility
models based on the mixture of multi-dimensional dynamics introduced by Brigo
et al. (2004).Comment: 16 page
Delta Effects in Pion-Nucleon Scattering and the Strength of the Two-Pion-Exchange Three-Nucleon Interaction
We consider the relationship between P-wave pi-N scattering and the strength
of the P-wave two-pion-exchange three-nucleon interaction (TPE3NI). We explain
why effective theories that do not contain the delta resonance as an explicit
degree of freedom tend to overestimate the strength of the TPE3NI. The
overestimation can be remedied by higher-order terms in these ``delta-less''
theories, but such terms are not yet included in state-of-the-art chiral EFT
calculations of the nuclear force. This suggests that these calculations can
only predict the strength of the TPE3NI to an accuracy of +/-25%.Comment: 13 pages, 2 figures, uses eps
Sensitivities for Bermudan Options by Regression Methods
In this article we propose several pathwise and finite difference based methods for calculating sensitivities of Bermudan options using regression methods and Monte Carlo simulation. These methods rely on conditional probabilistic representations which allow, in combination with a regression approach, for efficient simultaneous computation of sensitivities at many initial positions. Assuming that the price of a Bermudan option can be evaluated sufficiently accurate, we develop a method for constructing deltas based on least squares. We finally propose a testing procedure for assessing the performance of the developed methods.American and Bermudan options, Optimal stopping times, Monte Carlo simulation, Deltas, Conditional probabilistic representations, Regression methods
- …