Journal of Financial Economics Vol. 46 No. 3 1997
Bounds on contingent claims based on several assets
Abstract
In 1987, Lo derived an upper bound on the price of a European call option on a single asset. Lo's bound depends only on the mean and variance of the terminal asset price and is termed a semi-parametric bound. This paper derives similar semi-parametric bounds on a European call on the maximum of any number of assets. A distribution-free bound for the price of this option is obtained. The bound depends only on the means and covariance matrix of the returns on n underlying assets. The bound is obtained by optimizing over the entries of a positive definite matrix A. This can be accomplished by a technique known as semidefinite programming. We demonstrate the methodology using two specific applications. The first concerns the valuation of a European call option on the maximum of several assets. This is known as an outperformance option and is of some practical interest. The second application concerns the valuation of a discretely adjusted lookback option. These lookback options are of interest in connection with certain equity annuity insurance products.
- DOI
- 10.1016/s0304-405x(97)00035-4
- Volume
- 46
- Issue
- 3
- Pages
- 383-400
- Language
- en
- Sources
- bibtex:phds-export.bib openalex crossref