NDLI: Variance swaps on time-changed Lévy processes

Content Provider	Springer Nature Link
Author	Wu, Liuren Carr, Peter Lee, Roger
Copyright Year	2011
Abstract	We prove that a multiple of a log contract prices a variance swap, under arbitrary exponential Lévy dynamics, stochastically time-changed by an arbitrary continuous clock having arbitrary correlation with the driving Lévy process, subject to integrability conditions. We solve for the multiplier, which depends only on the Lévy process, not on the clock. In the case of an arbitrary continuous underlying returns process, the multiplier is 2, which recovers the standard no-jump variance swap pricing formula. In the presence of negatively skewed jump risk, however, we prove that the multiplier exceeds 2, which agrees with calibrations of time-changed Lévy processes to equity options data. Moreover, we show that discrete sampling increases variance swap values, under an independence condition; so if the commonly quoted multiple 2 undervalues the continuously sampled variance, then it undervalues even more the discretely sampled variance. Our valuations admit enforcement, in some cases, by hedging strategies which perfectly replicate variance swaps by holding log contracts and trading the underlying.
Ending Page	355
Page Count	21
Starting Page	335
File Format	PDF
ISSN	09492984
e-ISSN	14321122
Journal	Finance and Stochastics
Issue Number	2
Volume Number	16
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-03-24
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Time change Finance/Investment/Banking Statistics for Business/Economics/Mathematical Finance/Insurance Lévy process Variance swap Economic Theory Probability Theory and Stochastic Processes Quantitative Finance Processes with independent increments; LÃ©vy processes
Content Type	Text
Resource Type	Article
Subject	Finance Statistics and Probability Statistics, Probability and Uncertainty

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