Short Rate Models With Nonlinear Drift And Jumps
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| Author | : Amir Memartoluie |
| Publisher | : |
| Total Pages | : 91 |
| Release | : 2009 |
| Genre | : |
| ISBN | : |
Many financial contracts can be regarded as derivative securities where the underlying state variable is one or more rates of interest. A partial list of such contracts would include zero-coupon bonds, coupon paying bonds, callable bonds, convertible bonds, retractable/extendable bonds, etc., along with a number of popular interest rate derivatives such as swaps, swaptions, caps, and floors. A commonly used strategy for valuing these contracts is to base a continuous time model for the stochastic behaviour of the short term rate of interest. Three key features of most of the models currently in use are (i) the drift, or expected change over a short time period in the level of the short term interest rate, is a linear function; (ii) the conditional variance of changes in short term interest rates is not strongly related to the level of interest rates; and (iii) the short term interest rate is assumed to follow a diffusion process, which effectively means that it cannot change too rapidly over short periods of time. Each of these assumptions appears to be made primarily for modeling convenience, as they make it possible in some cases to derive analytical expressions for the values of bonds and European-style bond options. If such solutions are not available, then numerical techniques such as Monte Carlo simulation or the numerical solution of partial differential equations are needed. However, available econometric evidence indicates that all of the assumptions noted above are questionable: changes in short term interest rates may be characterized by drift which is nonlinear and by conditional variance that depends more heavily on the level of interest rates than is assumed in models with analytic solutions. Moreover, they may be better approximated by a jump-diffusion process which allows for sudden discontinuous changes. Consequently, it is of interest to develop numerical techniques to value interest rate derivative securities for cases where the short term interest rate follows a jump-diffusion process featuring non-linear drift. This thesis describes and illustrates the use of such techniques.
| Author | : Licheng Sun |
| Publisher | : |
| Total Pages | : |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
In this article I provide new evidence on the role of nonlinear drift and stochastic volatility in interest rate modeling. I compare various model specifications for the short-term interest rate using the data from five countries. I find that modeling the stochastic volatility in the short rate is far more important than specifying the shape of the drift function. The empirical support for nonlinear drift is weak with or without the stochastic volatility factor. Although a linear drift stochastic volatility model fits the international data well, I find that the level effect differs across countries.
| Author | : Hao Zhou |
| Publisher | : |
| Total Pages | : 52 |
| Release | : 2003 |
| Genre | : Interest rates |
| ISBN | : |
| Author | : Mark Cummins |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 213 |
| Release | : 2012-07-15 |
| Genre | : Mathematics |
| ISBN | : 1461434335 |
Presenting state-of-the-art methods in the area, the book begins with a presentation of weak discrete time approximations of jump-diffusion stochastic differential equations for derivatives pricing and risk measurement. Using a moving least squares reconstruction, a numerical approach is then developed that allows for the construction of arbitrage-free surfaces. Free boundary problems are considered next, with particular focus on stochastic impulse control problems that arise when the cost of control includes a fixed cost, common in financial applications. The text proceeds with the development of a fear index based on equity option surfaces, allowing for the measurement of overall fear levels in the market. The problem of American option pricing is considered next, applying simulation methods combined with regression techniques and discussing convergence properties. Changing focus to integral transform methods, a variety of option pricing problems are considered. The COS method is practically applied for the pricing of options under uncertain volatility, a method developed by the authors that relies on the dynamic programming principle and Fourier cosine series expansions. Efficient approximation methods are next developed for the application of the fast Fourier transform for option pricing under multifactor affine models with stochastic volatility and jumps. Following this, fast and accurate pricing techniques are showcased for the pricing of credit derivative contracts with discrete monitoring based on the Wiener-Hopf factorisation. With an energy theme, a recombining pentanomial lattice is developed for the pricing of gas swing contracts under regime switching dynamics. The book concludes with a linear and nonlinear review of the arbitrage-free parity theory for the CDS and bond markets.
| Author | : M.G. Akritas |
| Publisher | : Elsevier |
| Total Pages | : 523 |
| Release | : 2003-10-31 |
| Genre | : Mathematics |
| ISBN | : 0080540376 |
The advent of high-speed, affordable computers in the last two decades has given a new boost to the nonparametric way of thinking. Classical nonparametric procedures, such as function smoothing, suddenly lost their abstract flavour as they became practically implementable. In addition, many previously unthinkable possibilities became mainstream; prime examples include the bootstrap and resampling methods, wavelets and nonlinear smoothers, graphical methods, data mining, bioinformatics, as well as the more recent algorithmic approaches such as bagging and boosting. This volume is a collection of short articles - most of which having a review component - describing the state-of-the art of Nonparametric Statistics at the beginning of a new millennium.Key features:• algorithic approaches • wavelets and nonlinear smoothers • graphical methods and data mining • biostatistics and bioinformatics • bagging and boosting • support vector machines • resampling methods
| Author | : Eckhard Platen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 868 |
| Release | : 2010-07-23 |
| Genre | : Mathematics |
| ISBN | : 364213694X |
In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
| Author | : Qi Li |
| Publisher | : Emerald Group Publishing |
| Total Pages | : 570 |
| Release | : 2009-12-04 |
| Genre | : Business & Economics |
| ISBN | : 184950623X |
Contains a selection of papers presented initially at the 7th Annual Advances in Econometrics Conference held on the LSU campus in Baton Rouge, Louisiana during November 14-16, 2008. This work is suitable for those who wish to familiarize themselves with nonparametric methodology.
| Author | : David A. Chapman |
| Publisher | : |
| Total Pages | : |
| Release | : 1998 |
| Genre | : Derivative securities |
| ISBN | : |
| Author | : Peter Tankov |
| Publisher | : CRC Press |
| Total Pages | : 552 |
| Release | : 2003-12-30 |
| Genre | : Business & Economics |
| ISBN | : 1135437947 |
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
| Author | : Roberto Dieci |
| Publisher | : Springer |
| Total Pages | : 384 |
| Release | : 2014-07-26 |
| Genre | : Business & Economics |
| ISBN | : 3319074709 |
This book reflects the state of the art on nonlinear economic dynamics, financial market modelling and quantitative finance. It contains eighteen papers with topics ranging from disequilibrium macroeconomics, monetary dynamics, monopoly, financial market and limit order market models with boundedly rational heterogeneous agents to estimation, time series modelling and empirical analysis and from risk management of interest-rate products, futures price volatility and American option pricing with stochastic volatility to evaluation of risk and derivatives of electricity market. The book illustrates some of the most recent research tools in these areas and will be of interest to economists working in economic dynamics and financial market modelling, to mathematicians who are interested in applying complexity theory to economics and finance and to market practitioners and researchers in quantitative finance interested in limit order, futures and electricity market modelling, derivative pricing and risk management.
