NDLI: Discretely sampled variance and volatility swaps versus their continuous approximations

Content Provider	Springer Nature Link
Author	Kchia, Younes Larsson, Martin Protter, Philip Jarrow, Robert
Copyright Year	2012
Abstract	Discretely sampled variance and volatility swaps trade actively in OTC markets. To price these swaps, the continuously sampled approximation is often used to simplify the computations. The purpose of this paper is to study the conditions under which this approximation is valid. Our first set of theorems characterize the conditions under which the discretely sampled swap values are finite, given that the values of the continuous approximations exist. Surprisingly, for some otherwise reasonable price processes, the discretely sampled swap prices do not exist, thereby invalidating the approximation. Examples are provided. Assuming further that both swap values exist, we study sufficient conditions under which the discretely sampled values converge to their continuous counterparts. Because of its popularity in the literature, we apply our theorems to the 3/2 stochastic volatility model. Although we can show finiteness of all swap values, we can prove convergence of the approximation only for some parameter values.
Ending Page	324
Page Count	20
Starting Page	305
File Format	PDF
ISSN	09492984
e-ISSN	14321122
Journal	Finance and Stochastics
Issue Number	2
Volume Number	17
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-04-28
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Volatility swaps Finance/Investment/Banking Statistics for Business/Economics/Mathematical Finance/Insurance Signal detection and filtering Economic Theory Probability Theory and Stochastic Processes Semimartingales NFLVR Martingales with continuous parameter Variance swaps Quantitative Finance
Content Type	Text
Resource Type	Article
Subject	Finance Statistics and Probability Statistics, Probability and Uncertainty

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Discretely sampled variance and volatility swaps versus their continuous approximations

Discretely sampled variance and volatility swaps versus their continuous approximations (2011)

Hedging variance options on continuous semimartingales

The large-maturity smile for the Heston model

Shifting martingale measures and the birth of a bubble as a submartingale

Can the implied volatility surface move by parallel shifts?

The supermartingale property of the optimal wealth process for general semimartingales

Continuous-time trading and the emergence of probability

Market viability via absence of arbitrage of the first kind

Discretely sampled variance and volatility swaps versus their continuous approximations

Similar Documents

Discretely sampled variance and volatility swaps versus their continuous approximations

Discretely sampled variance and volatility swaps versus their continuous approximations (2011)

Hedging variance options on continuous semimartingales

The large-maturity smile for the Heston model

Shifting martingale measures and the birth of a bubble as a submartingale

Can the implied volatility surface move by parallel shifts?

The supermartingale property of the optimal wealth process for general semimartingales

Continuous-time trading and the emergence of probability

Market viability via absence of arbitrage of the first kind

Discretely sampled variance and volatility swaps versus their continuous approximations