Pricing and Upper Price Bounds of Relax Certificates

Review of Managerial Science, Forthcoming

30 Pages Posted: 5 Jul 2010

See all articles by Nicole Branger

Nicole Branger

University of Muenster - Finance Center Muenster

Antje Brigitte Mahayni

Mercator School of Management

Judith C. Schneider

University of Muenster - Finance Center Muenster

Date Written: July 1, 2010

Abstract

Relax certificates are written on multiple underlying stocks. Their payoff depends on a barrier condition and is thus path-dependent. As long as none of the underlying assets crosses a lower barrier, the investor receives the payoff of a coupon bond. Otherwise, there is a cash settlement at maturity which depends on the lowest stock return. Thus, the products consist of a knock-out coupon bond and a knock-in claim on the minimum of the stock prices. In a Black-Scholes model setup, the price of the knock-out part can be given in closed (or semi-closed) form in the case of one or two underlyings only. With the exception of the trivial case of one underlying, the price of the knock-in minimum claim always has to be calculated numerically. Hence, we derive semi-closed form upper price bounds. These bounds are the lowest upper price bounds which can be calculated without the use of numerical methods. In addition, the bounds are especially tight for the vast majority of relax certificates which are traded at a discount relative to the corresponding coupon bond. This is also illustrated with market data.

Keywords: Certificates, Barrier Option, Price Bounds

JEL Classification: G13

Suggested Citation

Branger, Nicole and Mahayni, Antje B. and Schneider, Judith C., Pricing and Upper Price Bounds of Relax Certificates (July 1, 2010). Review of Managerial Science, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1633414

Nicole Branger

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
Germany
+49 251 83 29779 (Phone)
+49 251 83 22867 (Fax)

HOME PAGE: http://www.wiwi.uni-muenster.de/fcm/fcm/das-finance-center/details.php?weobjectID=162

Antje B. Mahayni

Mercator School of Management ( email )

Lotharstraße 65
Duisburg, Nordrhein-Westfalen 47057
Germany

Judith C. Schneider (Contact Author)

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
Germany

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