Volatility Swap Under the SABR Model

TL;DR

This paper derives an analytical formula for the fair value of volatility swaps under the SABR model using confluent hypergeometric functions, verified through functional calculus, advancing quantitative pricing methods.

Contribution

It introduces an explicit analytical solution for volatility swap valuation within the SABR model framework, enhancing precision in financial derivatives pricing.

Findings

Analytical solution for volatility swap fair value derived

Solution verified with Rama Cont's functional calculus

Provides a new approach for SABR model-based pricing

Abstract

The SABR model is shortly presented and the volatility swap explained. The fair value for a volatility swap is then computed using the usual theory in financial mathematics. An analytical solution using confluent hypergeometric functions is found. The solution is then verified using Rama Cont's functional calculus.