Research PaperNo Access

CONSISTENT UPPER PRICE BOUNDS FOR EXOTIC OPTIONS

NICOLE BÄUERLE

Department of Mathematics, Karlsruhe Institute of Technology (KIT), Englerstr. 2, Karlsruhe 76131, Germany

E-mail Address: baeuerle@kit.edu

Corresponding author.

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DANIEL SCHMITHALS

Department of Mathematics, Karlsruhe Institute of Technology (KIT), Englerstr. 2, Karlsruhe 76131, Germany

E-mail Address: daniel.schmithals@kit.edu

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https://doi.org/10.1142/S0219024921500114Cited by:2 (Source: Crossref)

Abstract

We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that the (discounted) stock price process is a martingale under the no-arbitrage condition. In case the payoff is directionally convex we obtain the worst case marginal pricing measures. The speed of convergence of the upper price bound is determined when the number of observed stock prices increases. We illustrate our findings with some numerical computations.

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