Fourier-Laplace transforms in polynomial Ornstein-Uhlenbeck volatility models
We consider the Fourier-Laplace transforms of a broad class of polynomial Ornstein-Uhlenbeck (OU) volatility models, including the well-known Stein-Stein, Sch\"obel-Zhu, one-factor Bergomi, and the recently introduced Quintic OU models motivated by the SPX-VIX joint calibration problem. We show the connection between the joint Fourier-Laplace functional of the log-price and the integrated variance, and the solution of an infinite dimensional Riccati equation. Next, under some non-vanishing conditions of the Fourier-Laplace transforms, we establish an existence result for such Riccati equation and we provide a discretized approximation of the joint characteristic functional that is exponentially entire. On the practical side, we develop a numerical scheme to solve the stiff infinite dimensional Riccati equations and demonstrate the efficiency and accuracy of the scheme for pricing SPX options and volatility swaps using Fourier and Laplace inversions, with specific examples of the Quintic OU and the one-factor Bergomi models and their calibration to real market data.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
The quintic Ornstein-Uhlenbeck volatility model that jointly calibrates SPX & VIX smiles
The quintic Ornstein-Uhlenbeck volatility model is a stochastic volatility model where the volatility process is a polynomial function of degree five of a single Ornstein-Uhlenbeck process with fast mean reversion and la…
Valuing Exchange Options Under an Ornstein-Uhlenbeck Covariance Model
In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Pr…
Capturing Smile Dynamics with the Quintic Volatility Model: SPX, Skew-Stickiness Ratio and VIX
We introduce the two-factor Quintic Ornstein-Uhlenbeck model, where volatility is modeled as a polynomial of degree five based on the sum of two Ornstein-Uhlenbeck processes driven by the same Brownian Motion, each mean-…
The Generalized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and $Z$ Transforms
This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as…
European Power Option Pricing with Extended Vasicěk Interest Rate and Exponential Ornstein-Uhlenbeck Asset Process under Different Market Assumptions
We propose a general framework of European power option pricing under two different market assumptions about extended Vasic\v{e}k interest rate process and exponential Ornstein-Uhlenbeck asset process with continuous div…