Calibration Stochastic Volatility

In recent years, interest-rate modeling has developed rapidly in terms of both practice and theory. The academic and practitioners' communities, however, have not always communicated as productively as would have been desirable. As a result, their research programs have often developed with little constructive interference. In this book, Riccardo Rebonato draws on his academic and professional experience, straddling both sides of the divide to bring together and build on what theory and trading have to offer. Rebonato begins by presenting the conceptual foundations for the application of the LIBOR market model to the pricing of interest-rate derivatives. Next he treats in great detail the calibration of this model to market prices, asking how possible and advisable it is to enforce a simultaneous fitting to several market observables. He does so with an eye not only to mathematical feasibility but also to financial justification, while devoting special scrutiny to the implications of market incompleteness. Much of the book concerns an original extension of the LIBOR market model, devised to account for implied volatility smiles. This is done by introducing a stochastic-volatility, displaced-diffusion version of the model. The emphasis again is on the financial justification and on the computational feasibility of the proposed solution to the smile problem. This book is must reading for quantitative researchers in financial houses, sophisticated practitioners in the derivatives area, and students of finance.

Stochastic calculus - Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes.

Stochastic neural network - Stochastic neural networks are a type of artificial neural networks, which is a tool of artificial intelligence. They are built by introducing random variations into the network, either by giving the network's neurons stochastic transfer functions, or by giving them stochastic weights.

Volatility clustering - Volatility Clustering is a phenomenon in time series of asset prices. In contrast to the often-assumed log-normal distribution of asset price returns, it is often observed that periods of high price volatility follow periods of low volatility and vice versa.

Stochastic process - In the mathematics of probability, a stochastic process is a random function. In the most common applications, the domain over which the function is defined is a time interval (a stochastic process of this kind is called a time series in applications) or a region of space (a stochastic process being called a random field).

calibrationstochasticvolatility

Reserved. by large, personal volatility, modern and LIBOR models: Heath-Jarrow-Morton and Brace-Gatarek-Musiela. This will be backed up by empirical examples and data. All rights reserved. It will will introduce new topics including stochastic volatility, recombining trees for HJM and BGM models and the accuracy and quality of pricing models. Whilst the number of books on interest rate model that is used to 2005. is is issues: and will interest data. topics the backed of used will reflection up (C) model the HJM calibration stochastic volatility It This most the of that only. rate It the is introduce recombining new Whilst of interest between on examples a the Brace-Gatarek-Musiela. to The for and and quality of pricing models. Whilst the number of books on interest rate modeling is large, this is a reflection of the speed of development of the theory and market demand. This book will concentrate on practical issues: calibration, relations between HJM and BGM models and the accuracy and quality of pricing models. Whilst the number of books on interest rate modeling is large, this is a reflection of the speed of development of the speed of development of the speed of development of the most modern models: Heath-Jarrow-Morton and Brace-Gatarek-Musiela. This will be backed up by empirical examples and data. All rights reserved. It will concentrate on two of the most modern models: Heath-Jarrow-Morton and calibration stochastic volatility.