Variance Swap with Mean Reversion, Multifactor Stochastic Volatility and Jumps

Variance Swap with Mean Reversion, Multifactor Stochastic Volatility and Jumps
Author: Chi Seng Pun
Publisher:
Total Pages: 38
Release: 2020
Genre:
ISBN:
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This paper examines variance swap pricing using a model that integrates three major features of financial assets, namely the mean reversion in asset price, multi-factor stochastic volatility (SV) and simultaneous jumps in prices and volatility factors. Closed-form solutions are derived for vanilla variance swaps and gamma swaps while the solutions for corridor variance swaps and conditional variance swaps are expressed in a one-dimensional Fourier integral. The numerical tests confirm that the derived solution is accurate and efficient. Furthermore, empirical studies have shown that multi-factor SV models better capture the implied volatility surface from option data. The empirical results of this paper also show that the additional volatility factor contributes significantly to the price of variance swaps. Hence, the results favor multi-factor SV models for pricing variance swaps consistent with the implied volatility surface.

Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models

Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models
Author: Anatoliy V. Swishchuk
Publisher:
Total Pages: 26
Release: 2017
Genre:
ISBN:
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In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate volatility strikes and estimate VIX future prices. In empirical study, we use Markov chain Monte Carlo algorithm for model calibration based on S&P 500 historical data, evaluate the effect of adding jumps into asset price processes on volatility derivatives pricing, and compare the performance of different pricing approaches.

Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities

Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities
Author: Anatoli? Vital?evich Svishchuk
Publisher: World Scientific
Total Pages: 326
Release: 2013
Genre: Business & Economics
ISBN: 9814440132
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Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for different kinds of models and problems arising in financial and energy markets and the associated problems in modeling and pricing of a variety of swaps. The book also contains a study of a new model, the delayed Heston model, which improves the volatility surface fitting as compared with the classical Heston model. The author calculates variance and volatility swaps for this model and provides hedging techniques. The book considers content on the pricing of variance and volatility swaps and option pricing formula for mean-reverting models in energy markets. Some topics such as forward and futures in energy markets priced by multi-factor Levy models and generalization of Black-76 formula with Markov-modulated volatility are part of the book as well, and it includes many numerical examples such as S&P60 Canada Index, S&P500 Index and AECO Natural Gas Index.

Continuous Time Processes for Finance

Continuous Time Processes for Finance
Author: Donatien Hainaut
Publisher: Springer Nature
Total Pages: 359
Release: 2022-08-25
Genre: Mathematics
ISBN: 3031063619
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This book explores recent topics in quantitative finance with an emphasis on applications and calibration to time-series. This last aspect is often neglected in the existing mathematical finance literature while it is crucial for risk management. The first part of this book focuses on switching regime processes that allow to model economic cycles in financial markets. After a presentation of their mathematical features and applications to stocks and interest rates, the estimation with the Hamilton filter and Markov Chain Monte-Carlo algorithm (MCMC) is detailed. A second part focuses on self-excited processes for modeling the clustering of shocks in financial markets. These processes recently receive a lot of attention from researchers and we focus here on its econometric estimation and its simulation. A chapter is dedicated to estimation of stochastic volatility models. Two chapters are dedicated to the fractional Brownian motion and Gaussian fields. After a summary of their features, we present applications for stock and interest rate modeling. Two chapters focuses on sub-diffusions that allows to replicate illiquidity in financial markets. This book targets undergraduate students who have followed a first course of stochastic finance and practitioners as quantitative analyst or actuaries working in risk management.

Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate

Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate
Author: Jiling Cao
Publisher:
Total Pages: 16
Release: 2014
Genre:
ISBN:
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In this paper, we investigate the effects of imposing stochastic interest rate driven by the Cox-Ingersoll-Ross process along with the Heston stochastic volatility model for pricing variance swaps with discrete sampling times. A dimension reduction mechanism based on the framework of Little and Pant is applied which later reduces to solving sets of one-dimensional partial differential equation. A close form exact solution to the fair delivery price of a variance swap is obtained via derivation of characteristic functions. Practical implementation of this hybrid model is demonstrated through numerical simulations.

On the Valuation of Variance Swaps with Stochastic Volatility

On the Valuation of Variance Swaps with Stochastic Volatility
Author: Song-Ping Zhu
Publisher:
Total Pages: 0
Release: 2011
Genre:
ISBN:
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This paper is an extension to a recent paper Zhu and Lian (2009), in which a closed-form exact solution was presented for the price of variance swaps with a particular definition of the realized variance. Here, we further demonstrate that our approach is quite versatile and can be used for other definitions of the realized variance as well. In particular, we present a closed-form formula for the price of a variance swap with the realized variance in the payoff function being defined as a logarithmic return of the underlying asset at some pre-specified discretely sampling points. The simple formula presented here is a result of successfully finding an exact solution of the partial differential equation (PDE) system based on the Heston's (1993) two-factor stochastic volatility model. A distinguishable feature of this new solution is that the computational time involved in pricing variance swaps with discretely sampling time has been substantially improved.

A General Framework for Discretely Sampled Realized Variance Derivatives in Stochastic Volatility Models with Jumps

A General Framework for Discretely Sampled Realized Variance Derivatives in Stochastic Volatility Models with Jumps
Author: Zhenyu Cui
Publisher:
Total Pages: 43
Release: 2018
Genre:
ISBN:
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After the recent financial crisis, the market for volatility derivatives has expanded rapidly to meet the demand from investors, risk managers and speculators seeking diversification of the volatility risk. In this paper, we develop a novel and efficient transform-based method to price swaps and options related to discretely-sampled realized variance under a general class of stochastic volatility models with jumps. We utilize frame duality and density projection method combined with a novel continuous-time Markov chain (CTMC) weak approximation scheme of the underlying variance process. Contracts considered include discrete variance swaps, discrete variance options, and discrete volatility options. Models considered include several popular stochastic volatility models with a general jump size distribution: Heston, Scott, Hull-White, Stein-Stein, alpha-Hypergeometric, 3/2 and 4/2 models. Our framework encompasses and extends the current literature on discretely sampled volatility derivatives, and provides highly efficient and accurate valuation methods. Numerical experiments confirm our findings.