Asymptotic and exact pricing of options on variance

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

  • Martin Keller-Ressel - , Technische Universität Berlin (Autor:in)
  • Johannes Muhle-Karbe - , ETH Zurich (Autor:in)

Abstract

We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the small-time limits of options on both objects. We find that the difference between them strongly depends on whether or not the stock price process has jumps. Subsequently, we propose two new methods to evaluate the prices of options on the discretely sampled realized variance. One of the methods is approximative; it is based on correcting prices of options on quadratic variation by our asymptotic results. The other method is exact; it uses a novel randomization approach and applies Fourier-Laplace techniques. We compare the methods and illustrate our results by some numerical examples.

Details

OriginalspracheEnglisch
Seiten (von - bis)107-133
Seitenumfang27
FachzeitschriftFinance and stochastics
Jahrgang17
Ausgabenummer1
PublikationsstatusVeröffentlicht - Jan. 2013
Peer-Review-StatusJa
Extern publiziertJa

Externe IDs

ORCID /0000-0003-0913-3363/work/167706917

Schlagworte

Schlagwörter

  • Fourier-Laplace methods, Option pricing, Quadratic variation, Realized variance, Small-time asymptotics