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 The Hybrid Stochastic local Volatility Model with Applications in Pricing FX Options written by Yu Tian and published by . This book was released on 2013 with total page 264 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 A Hybrid Stochastic Volatility Model Incorporating Local Volatility written by Yu Tian and published by . This book was released on 2014 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present our study on a hybrid stochastic volatility model incorporating local volatility for pricing options in the foreign exchange (FX) market. The hybrid stochastic-local volatility model (SLV) could match the implied volatility surface well and meanwhile shows the flexibility for pricing exotic options. The difficulty in implementing the SLV model lies in the calibration of the leverage function, which can be roughly seen as a ratio between the local volatility and the conditional expectation of stochastic volatility. We will illustrate our implementation of the SLV model and show the pricing performance for exotic options.
Download or read book Investigation of the Effect of Using Stochastic and Local Volatility when Pricing Barrier Options written by and published by . This book was released on 2010 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Robust Static Super Replication of Barrier Options written by Jan H. Maruhn and published by Walter de Gruyter. This book was released on 2009-07-14 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Static hedge portfolios for barrier options are very sensitive with respect to changes of the volatility surface. To prevent potentially significant hedging losses this book develops a static super-replication strategy with market-typical robustness against volatility, skew and liquidity risk as well as model errors. Empirical results and various numerical examples confirm that the static superhedge successfully eliminates the risk of a changing volatility surface. Combined with associated sub-replication strategies this leads to robust price bounds for barrier options which are also relevant in the context of dynamic hedging. The mathematical techniques used to prove appropriate existence, duality and convergence results range from financial mathematics, stochastic and semi-infinite optimization, convex analysis and partial differential equations to semidefinite programming.
Download or read book Analytic Methods for Pricing Double Barrier Options in the Presence of Stochastic Volatility written by Oliver Faulhaber and published by . This book was released on 2002 with total page 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 A Chaos Expansion Approach Under Hybrid Volatility Models written by Hideharu Funahashi and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose an approximation method based on the Wiener-Ito chaos expansion for the pricing of European contingent claims. Our method is applicable to widely used option pricing models such as local volatility models, stochastic volatility models, and their combinations. This method is useful in practice since the resulting approximation formula is not computationally expensive, hence it is suitable for calibration purposes. We will show through some numerical examples that our approximation remains quite high even for the long maturity and/or the high volatility cases, which is a desired feature. As an example, we propose a hybrid volatility model and apply our approximation formula to the JPY/USD currency option market and obtain very accurate results.
Download or read book A Semi Group Expansion for Pricing Barrier Options written by Takashi Kato and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing barrier option in the log-normal SABR stochastic volatility model.
Download or read book An Asymptotic Expansion Formula for Up and Out Barrier Option Price Under Stochastic Volatility Model written by Takashi Kato and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate the validity of our approximation method through numerical examples.
Download or read book Local Volatility Under Stochastic Interest Rates Using Mixture Models written by Mark S. Joshi and published by . This book was released on 2016 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: A key requirement of any equity hybrid derivatives pricing model is the ability to rapidly and accurately calibrate to vanilla option prices. To this end, we present two methods for calibrating a local volatility model under correlated stochastic interest rates. This is achieved by first fitting a mixture model to market prices, and then determining the local volatility function that is consistent with this mixture model.
Download or read book A Unified Approach to Bermudan and Barrier Options Under Stochastic Volatility Models with Jumps written by Justin Kirkby and published by . This book was released on 2018 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Local Volatility written by Carol Alexander and published by . This book was released on 2008 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two unique volatility surfaces associated with any arbitrage-free set of standard European option prices, the implied volatility surface and the local volatility surface. Several papers have discussed the stochastic differential equations for implied volatilities that are consistent with these option prices but the static and dynamic no-arbitrage conditions are complex, mainly due to the large (or even infinite) dimensions of the state probability space. These no-arbitrage conditions are also instrument-specific and have been specified for some simple classes of options. However, the problem is easier to resolve when we specify stochastic differential equations for local volatilities instead. And the option prices and hedge ratios that are obtained by making local volatility stochastic are identical to those obtained by making instantaneous volatility or implied volatility stochastic. After proving that there is a one-to-one correspondence between the stochastic implied volatility and stochastic local volatility approaches, we derive a simple dynamic no-arbitrage condition for the stochastic local volatility model that is model-specific. The condition is very easy to check in local volatility models having only a few stochastic parameters.
Download or read book Fx Barriers With Smile Dynamics written by Glyn Baker and published by . This book was released on 2007 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our mandate in this work has been to isolate the features of smile consistent models that are most relevant to the pricing of barrier options. We consider the two classical approaches of stochastic and (parametric) local volatility. Although neither has been particularly successful in practice their differing qualitative features serve our exposition. By constructing approximate static hedges we are able to closely mimic their prices. The only information we require from the models, other than the initial vanilla market to which they are calibrated, is their conditional forward smile along the barrier. This strongly supports the fact that realistic smile dynamics are of paramount importance when assessing a model to be used in pricing barrier options.
Download or read book Stochastic Volatility Models with Applications to Option Pricing written by K. Khorasani and published by . This book was released on 1998 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
