Linear Quadratic Jump Diffusion Modelling With Application To Stochastic Volatility
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Author | : Peng Cheng |
Publisher | : |
Total Pages | : 60 |
Release | : 2003 |
Genre | : |
ISBN | : |
We aim at accommodating the existing affine jump-diffusion and quadratic models under the same roof, namely the linear-quadratic jump-diffusion (LQJD) class. We give a complete characterization of the dynamics underlying this class of models as well as identification constraints, and compute standard and extended transforms relevant to asset pricing. We also show that the LQJD class can be embedded into the affine class through use of an augmented state vector. We further establish that an equivalence relationship holds between both classes in terms of transform analysis. An option pricing application to multifactor stochastic volatility models reveals that adding nonlinearity into the model significantly reduces pricing errors, and further addition of a jump component in the stock price largely improves goodness-of-fit for in-the-money calls but less for out-of-the-money ones.
Author | : Floyd B. Hanson |
Publisher | : SIAM |
Total Pages | : 472 |
Release | : 2007-01-01 |
Genre | : Mathematics |
ISBN | : 9780898718638 |
This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems.
Author | : George J. Jiang |
Publisher | : |
Total Pages | : 13 |
Release | : 2012 |
Genre | : |
ISBN | : |
In this paper, we propose a unifying class of affine-quadratic term structure models (AQTSMs) in the general jump-diffusion framework. Extending existing term structure models, the AQTSMs incorporate random jumps of stochastic intensity in the short rate process. Using information from the Treasury futures market, we propose a GMM approach for the estimation of the risk-neutral process. A distinguishing feature of the approach is that the time series estimates of stochastic volatility and jump intensity are obtained, together with model parameter estimates. Our empirical results suggest that stochastic jump intensity significantly improves the model fit to the term structure dynamics. We identify a stochastic jump intensity process that is negatively correlated with interest rate changes. Overall, negative jumps tend to have a larger size than positive ones. Our empirical results also suggest that, at monthly frequency, while stochastic volatility has certain predictive power of inflation, jumps are neither triggered by nor predictive of changes in macroeconomic variables. At daily frequency, however, we document interesting patterns for jumps associated with informational shocks in the financial market.
Author | : Wei Wei |
Publisher | : |
Total Pages | : |
Release | : 2015 |
Genre | : |
ISBN | : |
Author | : Stefano Galluccio |
Publisher | : |
Total Pages | : 32 |
Release | : 2008 |
Genre | : |
ISBN | : |
In the context of arbitrage-free modelling of financial derivatives, we introduce a novel calibration technique for models in the affine-quadratic class for the purpose of over-the-counter option pricing and risk-management. In particular, we aim at calibrating a stochastic volatility jump diffusion model to the whole market implied volatility surface at any given time. We study the asymptotic behaviour of the moments of the underlying distribution and use this information to introduce and implement our calibration algorithm. We numerically show that the proposed approach is both statistically stable and accurate.
Author | : |
Publisher | : |
Total Pages | : 63 |
Release | : 2010 |
Genre | : |
ISBN | : |
Author | : Elisa Alós |
Publisher | : |
Total Pages | : |
Release | : 2008 |
Genre | : |
ISBN | : |
Author | : Mthuli Ncube |
Publisher | : |
Total Pages | : 124 |
Release | : 2012 |
Genre | : |
ISBN | : 9783659241192 |
Author | : Michail Korniotis |
Publisher | : |
Total Pages | : 179 |
Release | : 2009 |
Genre | : |
ISBN | : 9781109509427 |
We propose a multi-factor stochastic model that can be used as a modeling tool in several areas of applied mathematics. Our modeling efforts are focused on addressing the basic characteristics of quantities that represent random rate of change. These characteristics include properties of their evolution pattern, cross-factor correlation, and the stochastic nature of their diffusion parameter. At the same time, we address the question of solutions implied by the model, as well as the model's tractability. The model is introduced in a general mathematical context, prior to any specific problem consideration. We choose this approach to stress the model's functional independence of any particular application. Within this framework, we are able to represent the evolution of quantities sensitive to random rates of change, as solutions of partial differential equations. We obtain solutions of the resulting partial differential equations by adopting a two-step solution method. The first step approximates the solution using perturbation methods. This procedure specifies the two leading terms as solutions of simpler differential problems. The second step allows us to derive explicit solutions for the terms using the eigenfunction expansion method. A computer algorithm for the solution was also built. This allowed the calibration of the model parameters and a comparison of fitness with existing models. The usefulness and flexibility of the model is demonstrated by considering applications in three areas of applied mathematics: Interest rate, credit risk, and mortality modeling. We comment on how our model generalizes existing models in these areas and its advantages over previously proposed models.
Author | : Thomas More Arnold |
Publisher | : |
Total Pages | : 240 |
Release | : 1998 |
Genre | : |
ISBN | : |