New solvable stochastic volatility models for pricing volatility\n derivatives

2012/05/16 by Andrey Itkin, Itkin, Andrey
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1205.3550

openalex publication_date 2012/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Classical solvable stochastic volatility models (SVM) use a CEV process for\ninstantaneous variance where the CEV parameter \γ takes just few values:\n0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process,\n1- GARCH, and 3/2 - the 3/2 model. Some other models were discovered in\n citeLabordere2009 by making connection between stochastic volatility and\nsolvable diffusion processes in quantum mechanics. In particular, he used to\nbuild a bridge between solvable (super)potentials (the Natanzon\n(super)potentials, which allow reduction of a Schr "odinger equation to a\nGauss confluent hypergeometric equation) and existing SVM. In this paper we\ndiscuss another approach to extend the class of solvable SVM in terms of\nhypergeometric functions. Thus obtained new models could be useful for pricing\nvolatility derivatives (variance and volatility swaps, moment swaps).\n

Related

• Solvable Local and Stochastic Volatility Models: Supersymmetric Methods in Option Pricing
• From (Martingale) Schrodinger bridges to a new class of Stochastic\n Volatility Models
• The α-Hypergeometric Stochastic Volatility Model
• Quadratic Volatility from the Pöschl-Teller Potential and Hyperbolic Geometry
• Consistent Pricing of VIX and Equity Derivatives with the 4/2 Stochastic Volatility Plus Jumps Model