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.

Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate

Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate
Author: Teh Raihana Nazirah binti Roslan
Publisher:
Total Pages:
Release: 2016
Genre: Interest rate swaps
ISBN:

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Author supplied keywords: Variance swaps; Realized variance; Heston-CIR model; Volatility derivatives; Stochastic volatility; Stochastic interest rate.

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: Anatoliy Swishchuk
Publisher: World Scientific
Total Pages: 326
Release: 2013-06-03
Genre: Business & Economics
ISBN: 9814440140

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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.

Pricing Models of Volatility Products and Exotic Variance Derivatives

Pricing Models of Volatility Products and Exotic Variance Derivatives
Author: Yue Kuen Kwok
Publisher: CRC Press
Total Pages: 402
Release: 2022-05-08
Genre: Mathematics
ISBN: 1000584275

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Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods. Features Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products Can be used as a university textbook in a topic course on pricing variance derivatives

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 Closed-Form Exact Solution for Pricing Variance Swaps With Stochastic Volatility

A Closed-Form Exact Solution for Pricing Variance Swaps With Stochastic Volatility
Author: Song-Ping Zhu
Publisher:
Total Pages: 0
Release: 2012
Genre:
ISBN:

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In this paper, we present a highly efficient approach to price variance swaps with discrete sampling times. We have found a closed-form exact solution for the partial differential equation (PDE) system based on the Heston's two-factor stochastic volatility model embedded in the framework proposed by Little and Pant. In comparison with the previous approximation models based on the assumption of continuous sampling time, the current research of working out a closed-form exact solution for variance swaps with discrete sampling times at least serves for two major purposes: (i) to verify the degree of validity of using a continuous-sampling-time approximation for variance swaps of relatively short sampling period; (ii) to demonstrate that significant errors can result from still adopting such an assumption for a variance swap with small sampling frequencies or long tenor. Other key features of our new solution approach include the following: (1) with the newly found analytic solution, all the hedging ratios of a variance swap can also be analytically derived; (2) numerical values can be very efficiently computed from the newly found analytic formula.

Stochastic Volatility Modeling

Stochastic Volatility Modeling
Author: Lorenzo Bergomi
Publisher: CRC Press
Total Pages: 520
Release: 2015-12-16
Genre: Business & Economics
ISBN: 1482244071

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Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c

Financial Modelling with Jump Processes

Financial Modelling with Jump Processes
Author: Peter Tankov
Publisher: CRC Press
Total Pages: 552
Release: 2003-12-30
Genre: Business & Economics
ISBN: 1135437947

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WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic

Non-Parametric Pricing of Long-Dated Volatility Derivatives Under Stochastic Interest Rates

Non-Parametric Pricing of Long-Dated Volatility Derivatives Under Stochastic Interest Rates
Author: Mark S. Joshi
Publisher:
Total Pages: 25
Release: 2015
Genre:
ISBN:

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Although the effect of interest rate stochasticity can safely be ignored for short-dated exchange traded volatility derivatives, this is not the case for the kind of long-dated OTC derivatives often used by insurance companies and other financial institutions. We therefore extend existing model-free results for the pricing of variance swaps and more general volatility derivatives to account for stochastic interest rates, given certain independence and continuity assumptions. Finally, we present empirical examples to highlight the potential significance of this effect on long term contracts.

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.