A Lower Bound for the Volatility Swap in the Lognormal SABR Model-Reference-Cited by-同舟云学术

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A Lower Bound for the Volatility Swap in the Lognormal SABR Model

Published:2023-07-29 Issue:8 Volume:12 Page:749
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Alòs Elisa¹^ORCID,Rolloos Frido²,Shiraya Kenichiro³

Affiliation:

1. Barcelona Graduate School of Economics, Universitat Pompeu Fabra, 08005 Barcelona, Spain

2. Independent Researcher, 2500 The Hague, The Netherlands

3. Graduate School of Economics, The University of Tokyo, Tokyo 113-0033, Japan

Abstract

In the short time to maturity limit, it is proved that for the conditionally lognormal SABR model the zero vanna implied volatility is a lower bound for the volatility swap strike. The result is valid for all values of the correlation parameter and is a sharper lower bound than the at-the-money implied volatility for correlation less than or equal to zero.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/8/749/pdf

Reference7 articles.

1. Carr, P., and Lee, R. (2008, January 21). Robust replication of volatility derivatives. PRMIA award for Best Paper in Derivatives. Proceedings of the MFA 2008 Annual Meeting, New York, NY, USA.

2. Valuation of volatility derivatives as an inverse problem;Friz;Quant. Financ.,2005

3. Taylor-made volatility swaps;Rolloos;Wilmott,2017

4. On the difference between the volatility swap strike and the zero vanna implied volatility;Rolloos;Siam J. Financ. Math.,2021

5. Long memory in continuous-time stochastic volatility models;Comte;Math. Financ.,1998

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