1,413 research outputs found
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
Adjoint methods for computing sensitivities in local volatility surfaces
In this paper we present the adjoint method of computing sensitivities of option prices with respect to nodes in the local volatility surface. We first introduce the concept of algorithmic differentiation and how it relates to\ud
path-wise sensitivity computations within a Monte Carlo framework. We explain the two approaches available: forward mode and adjoint mode. We illustrate these concepts on the simple example of a model with a geometric Brownian motion driving the underlying price process, for which\ud
we compute the Delta and Vega in forward and adjoint mode. We then go on to explain in full detail how to apply these ideas to a model where the underlying has a volatility term defined by a local volatility surface. We provide source codes for both the simple and the more complex case and\ud
analyze numerical results to show the strengths of the adjoint approach
Derivatives Sensitivities Computation under Heston Model on GPU
This report investigates the computation of option Greeks for European and
Asian options under the Heston stochastic volatility model on GPU. We first
implemented the exact simulation method proposed by Broadie and Kaya and used
it as a baseline for precision and speed. We then proposed a novel method for
computing Greeks using the Milstein discretisation method on GPU. Our results
show that the proposed method provides a speed-up up to 200x compared to the
exact simulation implementation and that it can be used for both European and
Asian options. However, the accuracy of the GPU method for estimating Rho is
inferior to the CPU method. Overall, our study demonstrates the potential of
GPU for computing derivatives sensitivies with numerical methods
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