Skip to main content Accessibility help
×
Home

Superreplication of Options on Several Underlying Assets

  • Erik Ekström (a1), Svante Janson (a1) and Johan Tysk (a1)

Abstract

We investigate the conditions on a hedger, who overestimates the (time- and level-dependent) volatility, to superreplicate a convex claim on several underlying assets. It is shown that the classic Black-Scholes model is the only model, within a large class, for which overestimation of the volatility yields the desired superreplication property. This is in contrast to the one-dimensional case, in which it is known that overestimation of the volatility with any time- and level-dependent model guarantees superreplication of convex claims.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Superreplication of Options on Several Underlying Assets
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Superreplication of Options on Several Underlying Assets
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Superreplication of Options on Several Underlying Assets
      Available formats
      ×

Copyright

Corresponding author

Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden.
∗∗ Email address: ekstrom@math.uu.se

Footnotes

Hide All
∗∗∗

Partially supported by the Swedish Research Council.

Footnotes

References

Hide All
Avellaneda, M., Levy, A. and Parás, A. (1995). Pricing and hedging derivative securities in markets with uncertain volatilities. Appl. Math. Finance 2, 7388.
Bergenthum, J. and Rüschendorf, L. (2004). Comparison of option prices in semimartingale models. Preprint, Freiburg University.
Bergman, Y. Z., Grundy, D. B. and Wiener, Z. (1996). General properties of option prices. J. Finance 51, 15731610.
Ekström, E. (2004). Properties of American option prices. Stoch. Process. Appl. 114, 265278.
El Karoui, N., Jeanblanc-Picqué, M. and Shreve, S. (1998). Robustness of the Black and Scholes formula. Math. Finance 8, 93126.
Gozzi, F. and Vargiolu, T. (2002a). Superreplication of European multiasset derivatives with bounded stochastic volatility. Math. Meth. Operat. Res. 55, 6991.
Gozzi, F. and Vargiolu, T. (2002b). On the superreplication approach for European interest rate derivatives. In Seminar on Stochastic Analysis, Random Fields and Applications, III (Ascona, 1999; Progress Prob. 52), eds Dalang, R. C. and Russo, F., Birkhöuser, Basel, pp. 173188.
Hobson, D. (1998). Volatility misspecification, option pricing and superreplication via coupling. Ann. Appl. Prob.ö 8, 193205.
Janson, S. and Tysk, J. (2003). Volatility time and properties of option prices. Ann. Appl. Prob. 13, 890913.
Janson, S. and Tysk, J. (2004). Preservation of convexity of solutions to parabolic equations. J. Differential Equat. 206, 182226.
Karatzas, I. and Shreve, S. E. (1998). Methods of Mathematical Finance (Appl. Math. 39). Springer, New York.
Lyons, T. J. (1995). Uncertain volatility and the risk-free synthesis of derivatives. Appl. Math. Finance 2, 117133.
Martini, M. (1995). Propagation de la convexitö par des semi-groupes martingaliens sur la demi-droite. , Evry University.
Martini, M. (1999). Propagation of convexity by Markovian and martingalian semigroups. Potential Anal. 10, 133175.
Romagnoli, S. and Vargiolu, T. (2000). Robustness of the Black–Scholes approach in the case of options on several assets. Finance Stoch. 4, 325341.
Vargiolu, T. (2001). Existence, uniqueness and smoothness for the Black–Scholes–Barenblatt equation. Tech. Rep., Department of Tech. Rep.

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed