Static arbitrage bounds on basket option prices
type: Item
instance of: scholarly article
title: Static arbitrage bounds on basket option prices
zbMATH Open document ID: 1099.91067
author: Yanyan Li
published in: Mathematical Programming. Series A. Series B
publication date: 2006-06-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0302243
review text: Let \(p\in \mathbb R^m_+\), \(K_0\in \mathbb R_+\), \(w_0\in \mathbb R^n_{++}\) and \(K_i \in \mathbb R_+\), \(w_i\in \mathbb R^n_+\) for \(i=1,\dots,m\). The authors consider the problem of computing upper (resp. lower) bounds on the price of a European basket call option with maturity \(T\), strike \(K_0\) and weight vector \(w_0\): \[ \max/\min E_\pi[(w_0^Tx-K_0)_+]\text{ subject to }E_\pi[(w_i^Tx-K_i)_+]= p_i,\;i=1,\dots,m, \tag{*} \] over all probability distributions \(\pi\) on the asset price vector \(x\), consistent with a given set of observed prices \(p_i\) of options on other baskets. Here, (*) is thought of as an integral transform inversion problem. The authors detail a relaxation technique providing upper (resp. lower) bouns on the solution to (*). This technique has the advantage of being polynomial-time in the number of assets and constraints. In some particular cases, the authors provide exact solutions to (*) that have polynomial complexity on the number of assets and constraints.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 44A60
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C34
zbMATH DE Number: 5032422
zbMATH Keywords: Radon transform
zbMATH Keywords: Moment problems
reviewed by: Klaus Schürger
MaRDI profile type: Publication
OpenAlex ID: W2111246080
arXiv ID: math/0302243
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DOI: 10.1007/S10107-005-0642-Z
description: scientific article