A lattice algorithm for pricing moving average barrier options

Abstract

a b s t r a c tThis paper presents a lattice algorithm for pricing both European-and American-style moving average barrier options (MABOs). We develop a finite-dimensional partial differential equation (PDE) model for discretely monitored MABOs and solve it numerically by using a forward shooting grid method. The modeling PDE for continuously monitored MABOs has infinite dimensions and cannot be solved directly by any existing numerical method. We find their approximate values indirectly by using an extrapolation technique with the prices of discretely monitored MABOs. Numerical experiments show that our algorithm is very efficient.

Detrending moving average algorithm: Frequency response and scaling performances

“…For example in climatology, based on regular measurements from weather stations and satellite data, temperature trends are estimated both locally and globally [1][2][3][4]. In finance and economics, technical rules and visualization tools based on moving average trends are under continuous investigation and improvement [5][6][7][8]. A main issue in the application of trend estimates is related to the assumption of the model describing the underlying evolution process (e.g.…”

High-Dimensional Regression on Sparse Grids Applied to Pricing Moving Window Asian Options

“…It gives a more efficient selection of basis functions. This technique has been successfully applied in the field of high-dimensional function approximations [15] and many others [10,13,16,18].…”

“…The idea of sparse grid was originally discovered by Smolyak [8] and was rediscovered by Zenger [9] for PDE solutions in 1990. Since then, it has been applied to many different topics, such as integration [10,11] or Fast Fourier Transform (FFT) [12]. Sparse grids have also been used for finite element PDE solutions by Bungartz [13], interpolation by Bathelmann et al [14], clustering by Garcke et al [15], and PDE option pricing by Reisinger [16].…”

A Finite-Dimensional Approximation for Pricing Moving Average Options

“…This is known as Laguerre approximation, because for a fixed p, the first n scaled Laguerre functions (defined below) form an orthonormal basis of the space of all functions of the form (7) endowed with the scalar product of L 2 ([0, ∞)) which will be denoted by ·, · . See [18] for a discussion of optimality of Laguerre approximations among all approximations of type (6).…”

“…Indeed, this tree-based approach leads to an algorithm complexity (number of tree nodes) which exponentially increases with the number of time steps in the averaging period. Finally, Dai et al [6] introduce a lattice algorithm for pricing Bermudan moving average barrier options. The authors propose a finite dimensional PDE model for such options and solve it using a grid method.…”