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Author: Jiling Cao Publisher: ISBN: Category : Languages : en Pages : 16
Book Description
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.
Author: Jiling Cao Publisher: ISBN: Category : Languages : en Pages : 16
Book Description
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.
Author: Anatoliy Swishchuk Publisher: World Scientific ISBN: 9814440140 Category : Business & Economics Languages : en Pages : 326
Book Description
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.
Author: Song-Ping Zhu Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Nicolas Privault Publisher: World Scientific ISBN: 9812832734 Category : Science Languages : en Pages : 191
Book Description
This textbook is written as an accessible introduction to interest rate modeling and related derivatives, which have become increasingly important subjects of interest in financial mathematics. The models considered range from standard short rate to forward rate models and include more advanced topics such as the BGM model and an approach to its calibration. An elementary treatment of the pricing of caps and swaptions under forward measures is also provided, with a focus on explicit calculations and a step-by-step introduction of concepts. Each chapter is accompanied with exercises and their complete solutions, making this book suitable for advanced undergraduate or beginning graduate-level students.
Author: Anatoliy V. Swishchuk Publisher: ISBN: Category : Languages : en Pages : 26
Book Description
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.
Author: Song-Ping Zhu Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Alex Badescu Publisher: ISBN: Category : Languages : en Pages : 38
Book Description
In this article, we investigate the pricing and convergence of general non-affine non-Gaussian GARCH-based variance swap prices. Explicit solutions for fair strike prices under two different sampling schemes are derived using the extended Girsanov principle as our pricing kernel candidate. Following standard assumptions on the time-varying GARCH parameters, we show that these quantities converge to discretely and continuously sampled variance swaps constructed based on the weak diffusion limit of the underlying GARCH model. An empirical study which relies on a joint estimation using both historical returns and VIX data indicates that an asymmetric heavier-tailed distribution is more appropriate for modelling the GARCH innovations. Finally, we provide several numerical exercises to support our theoretical convergence results in which we investigate the effect of the quadratic variation approximation for the realized variance, as well as the impact of discrete versus continuous-time modelling of asset returns.
Author: Jiling Cao
Author: Jiling Cao
Author: Anatoliy Swishchuk
Author: Teh Raihana Nazirah binti Roslan
Author: Song-Ping Zhu
Author: Antoine Petrus Cornelius van der Ploeg
Author: Nicolas Privault
Author: Ke Chen (Economist)
Author: Anatoliy V. Swishchuk
Author: Song-Ping Zhu
Author: Alex Badescu