General closed-form basket option pricing bounds

Caldana, R., Fusai, G., Gnoatto, A. & Grasselli, M. (2016). General closed-form basket option pricing bounds. Quantitative Finance, 16(4), pp. 535-554. doi: 10.1080/14697688.2015.1073854

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Abstract

This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms; hence, they do not suffer from the curse of dimensionality and can be applied also to high-dimensional problems where most existing methods fail. In particular, we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate.

Item Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 14 Sep 2015, available online: http://www.tandfonline.com/10.1080/14697688.2015.1073854
Uncontrolled Keywords: Basket option, Option pricing, Fourier inversion, Control variate
Subjects: H Social Sciences > HG Finance
Divisions: Cass Business School > Faculty of Finance
URI: http://openaccess.city.ac.uk/id/eprint/15729

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