Abstract
This article exploits arbitrage valuation bounds on currency basket options. Instead of using a sophisticated model to price these options, we consider a set of pricing models that are consistent with the prices of available hedging assets. In the absence of arbitrage, we identify valuation bounds on currency basket options without model specifications. Our results extend the work in the literature by seeking tight arbitrage valuation bounds on these options. Specifically, the valuation bounds are enforced by static portfolios that consist of both cross-currency options and individual options denominated in the numeraire currency.
Highlights
For many corporations and financial institutions, basket options are an important tool in managing currency exposures
We find that the valuation bounds on currency basket options could be further tightened when the cross-currency options are incorporated
Basket options are traded as alternative instruments to manage risk exposure in multiple underlying assets
Summary
For many corporations and financial institutions, basket options are an important tool in managing currency exposures. Laurence and Wang (2005) [21] investigate the relation between pricing and hedging basket options In these three papers, valuation bounds on basket options with two underlying assets may be expressed analytically. In Hobson, Laurence and Wang (2005a, 2005b) [22,23], the arbitrage bounds on basket options in a general setup are derived using portfolios of options on individual underlying assets with the number of n ≥ 2. These studies extend the results of Laurence and Wang (2005) [21] when traded options are available at a continuum of strike prices.
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