Download or read book The Heston Stochastic Volatility Model with Piecewise Constant Parameters Efficient Calibration and Pricing of Window Barrier Options written by Daniel Guterding and published by . This book was released on 2019 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a simple and numerically efficient approach to the calibration of the Heston stochastic volatility model with piecewise constant parameters. Extending the original ansatz for the characteristic function, proposed in the seminal paper by Heston, to the case of piecewise constant parameters, we show that the resulting set of ordinary differential equations can still be integrated semi-analytically. Our numerical scheme is based on the calculation of the characteristic function using Gauss-Kronrod quadrature, additionally supplying a Black-Scholes control variate to stabilize the numerical integrals. We apply our method to the problem of calibration of the Heston model with piecewise constant parameters to the foreign exchange (FX) options market. Finally, we demonstrate cases in which window barrier option prices calculated using the Heston model with piecewise constant parameters are consistent with the market, while those calculated with a plain Heston model are not.
Download or read book Barrier Options Pricing in the Heston Stochastic Volatility Model written by Vitalija Alisauskaite and published by . This book was released on 2010 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Valuation of Fader and Discrete Barrier Options in Heston s Stochastic Volatility Model written by Susanne Griebsch and published by . This book was released on 2010 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We focus on closed-form option pricing in Heston's stochastic volatility model, where closed-form formulas exist only for a few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this closed-form approach and derive multivariate characteristic functions depending on at least two spot values for different points in time. The derived characteristic functions are used as building blocks to set up (semi-) analytical pricing formulas for exotic options with payoffs depending on finitely many spot values such as fader options and discretely monitored barrier options. We compare our result with different numerical methods and examine accuracy and computational times.
Download or read book The Heston Stochastic Local Volatility Model written by Anthonie van der Stoep and published by . This book was released on 2018 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a non-parametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by Dupire (1994) and Derman & Kani (1998). In particular, the additional local volatility component acts as a "compensator" that bridges the mismatch between the non-perfectly calibrated Heston model and the market quotes for European-type options. By means of numerical experiments we show that our scheme enables a consistent and fast pricing of products that are sensitive to the forward volatility skew. Detailed error analysis is also provided.
Download or read book An Analysis of the Heston Stochastic Volatility Model written by Ricardo Crisóstomo and published by . This book was released on 2016 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper analyses the implementation and calibration of the Heston Stochastic Volatility Model. We first explain how characteristic functions can be used to estimate option prices. Then we consider the implementation of the Heston model, showing that relatively simple solutions can lead to fast and accurate vanilla option prices. We also perform several calibration tests, using both local and global optimization. Our analyses show that straightforward setups deliver good calibration results. All calculations are carried out in Matlab and numerical examples are included in the paper to facilitate the understanding of mathematical concepts.
Download or read book The Hybrid Stochastic Local Volatility Model with Applications in Pricing FX Options written by Yu Tian and published by . This book was released on 2016 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes. On the other hand, the local volatility model can reproduce the implied volatility surface, whereas it does not consider the stochastic behaviour of the volatility. To combine the advantages of stochastic volatility (SV) and local volatility (LV) models, a class of stochastic-local volatility (SLV) models has been developed. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The leverage function can be roughly seen as a ratio between local volatility and conditional expectation of stochastic volatility. The difficulty of implementing the SLV model lies in the calibration of the leverage function. In the thesis, we first review the fundamental theories of stochastic differential equations and the classic option pricing models, and study the behaviour of the volatility in the context of FX market. We then introduce the SLV model and illustrate our implementation of the calibration and pricing procedure. We apply the SLV model to exotic option pricing in the FX market and compare pricing results of the SLV model with pure local volatility and pure stochastic volatility models. Numerical results show that the SLV model can match the implied volatility surface very well as well as improve the pricing performance for barrier options. In addition, we further discuss some extensions of the SLV project, such as parallelization potential for accelerating option pricing and pricing techniques for window barrier options. Although the SLV model we use in the thesis is not entirely new, we contribute to the research in the following aspects: 1) we investigate the hybrid volatility modeling thoroughly from theoretical backgrounds to practical implementations; 2) we resolve some critical issues in implementing the SLV model such as developing a fast and stable numerical method to derive the leverage function; and 3) we build a robust calibration and pricing platform under the SLV model, which can be extended for practical uses.
Download or read book Efficient Simulation of the Heston Stochastic Volatility Model written by Leif B. G. Andersen and published by . This book was released on 2007 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility models are increasingly important in practical derivatives pricing applications, yet relatively little work has been undertaken in the development of practical Monte Carlo simulation methods for this class of models. This paper considers several new algorithms for time-discretization and Monte Carlo simulation of Heston-type stochastic volatility models. The algorithms are based on a careful analysis of the properties of affine stochastic volatility diffusions, and are straightforward and quick to implement and execute. Tests on realistic model parameterizations reveal that the computational efficiency and robustness of the simulation schemes proposed in the paper compare very favorably to existing methods.
Download or read book Pricing Window Barrier Options with a Hybrid Stochastic Local Volatility Model written by Yu Tian and published by . This book was released on 2014 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present our research on pricing window barrier options under a hybrid stochastic-local volatility (SLV) model in the foreign exchange (FX) market. Due to the hybrid effect of the local volatility and stochastic volatility components of the model, the SLV model can reproduce the market implied volatility surface, and can improve the pricing accuracy for exotic options at the same time. In this paper, numerical techniques such as Monte Carlo and finite difference methods for standard exotic barrier options under the SLV model are extended to pricing window barrier options and numerical results produced by the SLV model are used to examine the performance and accuracy of the model for pricing window barrier options.
Download or read book Efficient Almost Exact Simulation of the Heston Stochastic Volatility Model written by Alexander van Haastrecht and published by . This book was released on 2011 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: We deal with several efficient discretization methods for the simulation of the Heston stochastic volatility model. The resulting schemes can be used to calculate all kind of options and corresponding sensitivities, in particular the exotic options that cannot be valued with closed-form solutions. We focus on to the (computational) efficiency of the simulation schemes: though the Broadie and Kaya (2006) paper provided an exact simulation method for the Heston dynamics, we argue why its practical use might be limited. Instead we consider efficient approximations of the exact scheme, which try to exploit certain distributional features of the underlying variance process. The resulting methods are fast, highly accurate and easy to implement. We conclude by numerically comparing our new schemes to the exact scheme of Broadie and Kaya, the almost exact scheme of Smith, the Kahl-Jackel scheme, the Full Truncation scheme of Lord et al. and the Quadratic Exponential scheme of Andersen.
Download or read book Local Stochastic Volatility Models written by Cristian Homescu and published by . This book was released on 2014 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze in detail calibration and pricing performed within the framework of local stochastic volatility LSV models, which have become the industry market standard for FX and equity markets. We present the main arguments for the need of having such models, and address the question whether jumps have to be included. We include a comprehensive literature overview, and focus our exposition on important details related to calibration procedures and option pricing using PDEs or PIDEs derived from LSV models. We describe calibration procedures, with special attention given to usage and solution of corresponding forward Kolmogorov PDE/PIDE, and outline powerful algorithms for estimation of model parameters. Emphasis is placed on presenting practical details regarding the setup and the numerical solution of both forward and backward PDEs/PIDEs obtained from the LSV models. Consequently we discuss specifics (based on our experience and best practices from literature) regarding choice of boundary conditions, construction of nonuniform spatial grids and adaptive temporal grids, selection of efficient and appropriate finite difference schemes (with possible enhancements), etc. We also show how to practically integrate specific features of various types of financial instruments within calibration and pricing settings. We consider all questions and topics identified as most relevant during the selection, calibration and pricing procedures associated with local stochastic volatility models, providing answers (to the best of our knowledge), and present references for deeper understanding and for additional perspectives. In a nutshell, it is our intention to present here an effective roadmap for a successful LSV journey.
Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimation of a Stochastic Volatility Model Using Pricing and Hedging Information written by Jason Fink and published by . This book was released on 2005 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimation of option pricing models in which the underlying asset exhibits stochastic volatility presents complicated econometric questions. One such question, thus far unstudied, is whether the inclusion of information derived from hedging relationships implied by an option pricing model may be used in conjunction with pricing information to provide more reliable parameter estimates than the use of pricing information alone. This paper estimates, using a simple least-squares procedure, the stochastic volatility model of Heston (1993), and includes hedging information in the objective function. This hedging information enters the objective function through a weighting parameter that is chosen optimally within the model. With the weight appropriately chosen, we find that incorporating the hedging information reduces both the out-of-sample hedging and pricing errors associated with the Heston model.
Download or read book Pricing and Risk Management with Stochastic Volatility Using Importance Sampling written by Przemyslaw Stan Stilger and published by . This book was released on 2014 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract In this paper, we apply importance sampling to Heston's stochastic volatility model and Bates's stochastic volatility model with jumps. We propose an effective numerical scheme that dramatically improves the speed of importance sampling. We show how the Greeks can be computed using the Likelihood Ratio Method based on characteristic function, and how combining it with importance sampling leads to a significant variance reduction for the Greeks. All results are illustrated using European and barrier options.
Download or read book Computing Journal written by Anna Pretre and published by . This book was released on 2015 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we compare different models describing the implied volatility surface. In particular we analyse in-depth the numerical properties of the Heston model and we extend it to include Jump processes. In our approach, we first identify a closed-form solution or a closest proxy of it, we then price contingent claims testing correctness and efficiency of the numerical solution against the closed-form solution, finally the numerical solution is adapted to American-option pricing.For each model, the closed-form solution is obtained from the stochastic differential equation and the numerical solution is worked out from the integropartial-differential equation. In all cases the scaling behavior and the effective parameter range in practical cases is addressed.
Download or read book Efficient Pricing Barrier Options and CDS in L vy Models with Stochastic Interest Rate written by Svetlana Boyarchenko and published by . This book was released on 2015 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, advantages of conformal deformations of the contours of integration in pricing formulas for European options have been demonstrated in the context of wide classes of L'evy models, the Heston model and other affine models. Similar deformations were used in one-factor L'evy models to price options with barrier and lookback features and CDSs. In the present paper, we generalize this approach to models of structural default, where the dynamics of assets follows an exponential L'evy process $X_t$, and the interest rate $r_t$ is stochastic. Assuming that $X_t$ and $r_t$ are independent, and the infinitesimal generator of the pricing semigroup in the model for the short rate, is (block)-diagonalizable, we develop a variation of the pricing procedure for L'evy models which is almost as fast as in the case of the constant interest rate. Numerical examples show that about 0.15 sec suffice to calculate prices of 8 options of same maturity in a two-factor model with the error tolerance $5 cdot 10^{-5}$ sec. and less; in a three-factor model, accuracy of order 0.001-0.005 is achieved in about 0.2 sec. Similar results are obtained for quanto CDS, where an additional stochastic factor is the exchange rate. We suggest a class of L'evy models with the stochastic interest rate driven by 1-2 (possibly, 3) factors, which allows for fast calculations. This class can satisfy the current requirements by regulators for banks to have sufficiently sophisticated credit risk models.
Download or read book Exotic Option Pricing in Heston s Stochastic Volatility Model written by Susanne A. Griebsch and published by . This book was released on 2008 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Performance of Popular Stochastic Volatility Option Pricing Models During the Subprime Crisis written by Thibaut Moyaert and published by . This book was released on 2016 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using daily options prices on the Eurostoxx 50 stock index over the whole year 2008, we compare the performance of three popular stochastic volatility models (Heston, 1993; Bates, 1996; Heston and Nandi, 2'007, in addition to the traditional Black-Scholes model and a proprietary trading desk model. We show that the most consistent in-sample and out-of-sample statistical performance is obtained for the internal model. However, the Bates model seems to be better suited to short term (out-of-the-money) options while the Heston model seems to perform better for medium or long term options. In terms of hedging performance, the Heston and Nandi model exhibits the best average, albeit most volatile, result and the Heston model outperforms the Black and Scholes model in terms of hedging errors, mainly for option contracts that mature in-the-money.
