EconStor >
Goethe-Universität Frankfurt am Main >
Fachbereich Wirtschaftswissenschaften, Universität Frankfurt a. M. >
Working Paper Series: Finance and Accounting, Universität Frankfurt a. M. >

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10419/23403
  
Title:When are Static Superhedging Strategies Optimal? PDF Logo
Authors:Branger, Nicole
Esser, Angelika
Schlag, Christian
Issue Date:2004
Series/Report no.:Working paper series / Johann-Wolfgang-Goethe-Universität Frankfurt am Main, Fachbereich Wirtschaftswissenschaften : Finance & Accounting 138
Abstract:This paper deals with the superhedging of derivatives on incomplete markets, i.e. with portfolio strategies which generate payoffs at least as high as that of a given contingent claim. The simplest solution to this problem is in many cases a static superhedge, i.e. a buy-and-hold strategy generating an affine-linear payoff. We study whether a superhedge can be achieved with less initial capital if we also allow for dynamic trading strategies. The answer to this question depends on the kind of the non-traded risk factors. Our main findings for a stochastic volatility model with unbounded volatility show that there is always an optimal static su- perhedge. Additionally, there may be infinitely many optimal dynamic superhedges which require the same initial capital. In a model with stochastic jumps, it is always either a dynamic or a static strategy which is optimal, but never both. In a model with a stochastic short rate the properties of the interest rate process are also rele- vant. When there are no bounds for the interest rate optimal superhedges (if they exist) are always static, since the strategy will never contain an investment in the money market account. On the other hand, when interest rates are either bounded or non-negative either a static or a dynamic strategy is optimal, depending on the respective contingent claim. Our results have important implications for the design of superhedges as they show under which conditions we can restrict the analysis to static strategies. There is no such thing as the incomplete market when it comes to superhedging. Although in continuous-time models the class of possible trading strategies contains much more elements than just static strategies, there is a number of cases where buy-and-hold is as good as or even superior to dynamic strategies.
Subjects:Incomplete markets
superhedging
stochastic volatility
stochastic jumps
stochastic interest rates
JEL:G13
Document Type:Working Paper
Appears in Collections:Working Paper Series: Finance and Accounting, Universität Frankfurt a. M.

Files in This Item:
File Description SizeFormat
404.pdf206.52 kBAdobe PDF
No. of Downloads: Counter Stats
Download bibliographical data as: BibTeX
Share on:http://hdl.handle.net/10419/23403

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.