Efficient Estimation of Lower and Upper Bounds for Pricing Higher-Dimensional American Arithmetic Average Options by Approximating Their Payoff Functions

42 Pages Posted: 31 Jan 2015

See all articles by Xing Jin

Xing Jin

University of Warwick - Warwick Business School

Cheng-Yu Yang

University of Warwick, Warwick Business School

Date Written: January 28, 2015

Abstract

In this paper, we develop an efficient payoff function approximation approach to estimating lower and upper bounds for pricing American arithmetic average options with a large number of underlying assets. The crucial step in the approach is to find a geometric mean which is more tractable than and highly correlated with a given arithmetic mean. Then the optimal exercise strategy for the resultant American geometric average option is used to obtain a low-biased estimator for the corresponding American arithmetic average option. This method is particularly efficient for the asset prices modeled by jump-diffusion processes with deterministic volatilities because the geometric mean is always a one-dimensional Markov process regardless of the number of underlying assets and thus is free from the curse of dimensionality. Another appealing feature of our method is that it provides an extremely efficient way to obtain tight upper bounds with no nested simulation involved as opposed to some existing duality approaches. Various numerical examples with up to 100 underlying stocks suggest that our algorithm is able to produce computationally efficient results.

Keywords: American arithmetic average option, Optimal exercise time, Arithmetic average, Geometric average, Dimension reduction

JEL Classification: G13

Suggested Citation

Jin, Xing and Yang, Cheng-Yu, Efficient Estimation of Lower and Upper Bounds for Pricing Higher-Dimensional American Arithmetic Average Options by Approximating Their Payoff Functions (January 28, 2015). Available at SSRN: https://ssrn.com/abstract=2558439 or http://dx.doi.org/10.2139/ssrn.2558439

Xing Jin (Contact Author)

University of Warwick - Warwick Business School ( email )

Gibbet Hill Rd.
Coventry, West Midlands CV4 8UW
United Kingdom

Cheng-Yu Yang

University of Warwick, Warwick Business School ( email )

West Midlands, CV4 7AL
United Kingdom

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
112
Abstract Views
910
Rank
415,839
PlumX Metrics