Non Parametric Pricing Of Long Dated Volatility Derivatives Under Stochastic Interest Rates
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Non Parametric Pricing Of Long Dated Volatility Derivatives Under Stochastic Interest Rates
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Author : Mark S. Joshi
language : en
Publisher:
Release Date : 2015
Non Parametric Pricing Of Long Dated Volatility Derivatives Under Stochastic Interest Rates written by Mark S. Joshi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Although the effect of interest rate stochasticity can safely be ignored for short-dated exchange traded volatility derivatives, this is not the case for the kind of long-dated OTC derivatives often used by insurance companies and other financial institutions. We therefore extend existing model-free results for the pricing of variance swaps and more general volatility derivatives to account for stochastic interest rates, given certain independence and continuity assumptions. Finally, we present empirical examples to highlight the potential significance of this effect on long term contracts.
Nonparametric Pricing Of Interest Rate Derivative Securities
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Author : Yacine Aït-Sahalia
language : en
Publisher:
Release Date : 1995
Nonparametric Pricing Of Interest Rate Derivative Securities written by Yacine Aït-Sahalia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Derivative securities categories.
We propose a nonparametric estimation procedure for continuous- time stochastic models. Because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process, we leave the volatility function unrestricted and estimate it nonparametrically. Only discrete data are used but the estimation procedure still does not rely on replacing the continuous- time model by some discrete approximation. Instead the drift and volatility functions are forced to match the densities of the process. We estimate the stochastic differential equation followed by the short term interest rate and compute nonparametric prices for bonds and bond options.
Nonparametric Pricing Of Interest Rate Derivative Securities
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Author : Yacine Ait-Sahalia
language : en
Publisher:
Release Date : 2010
Nonparametric Pricing Of Interest Rate Derivative Securities written by Yacine Ait-Sahalia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
We propose a nonparametric estimation procedure for continuous- time stochastic models. Because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process, we leave the volatility function unrestricted and estimate it nonparametrically. Only discrete data are used but the estimation procedure still does not rely on replacing the continuous- time model by some discrete approximation. Instead the drift and volatility functions are forced to match the densities of the process. We estimate the stochastic differential equation followed by the short term interest rate and compute nonparametric prices for bonds and bond options.
Pricing Of Long Dated Commodity Derivatives With Stochastic Volatility And Stochastic Interest Rates
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Author : Benjamin Cheng
language : en
Publisher:
Release Date : 2016
Pricing Of Long Dated Commodity Derivatives With Stochastic Volatility And Stochastic Interest Rates written by Benjamin Cheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Aiming to study pricing of long-dated commodity derivatives, this paper presents a class of models within the Heath, Jarrow, and Morton (1992) framework for commodity futures prices that incorporates stochastic volatility and stochastic interest rate and allows a correlation structure between the futures price process, the futures volatility process and the interest rate process. The functional form of the futures price volatility is specified so that the model admits finite dimensional realisations and retains affine representations, henceforth quasi-analytical European futures option pricing formulae can be obtained. A sensitivity analysis reveals that the correlation between the interest rate process and the futures price process has noticeable impact on the prices of long-dated futures options, while the correlation between the interest rate process and the futures price volatility process does not impact option prices. Furthermore, when interest rates are negatively correlated with futures prices then option prices are more sensitive to the volatility of interest rates, an effect that is more pronounced with longer maturity options.
Stochastic Volatility And The Pricing Of Financial Derivatives
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Author : Antoine Petrus Cornelius van der Ploeg
language : en
Publisher: Rozenberg Publishers
Release Date : 2006
Stochastic Volatility And The Pricing Of Financial Derivatives written by Antoine Petrus Cornelius van der Ploeg and has been published by Rozenberg Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
A Comparison Of Fixed Income Valuation Models
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Author : Michael Jacobs
language : en
Publisher:
Release Date : 2007
A Comparison Of Fixed Income Valuation Models written by Michael Jacobs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
This study compares continuous-time stochastic interest rate and stochastic volatility models of interest rate derivatives, examining these models across several dimensions: different classes of models, factor structures, and pricing algorithms. We consider a broader universe of pricing models, using improved econometric and numerical methodologies. We establish several criteria for model quality that are motivated by financial theory as well as practice: realism of the assumed stochastic process for the term structure, consistency with no-arbitrage or financial market equilibrium, consistency with financial practice, parsimony, as well as computational efficiency. A model which scores well along these grounds will also exhibit superior pricing performance with regard to traded interest rate options. This helps resolve the controversies over the stochastic process for yield curve dynamics, the models that best manage and measure interest rate risk, and theories of the term structure that are supported by empirical results. We perform econometric experiments at three levels: the short rate, bond prices, as well as interest rate derivatives. We extend CKLS (1992) to a broader class of single factor spot rate models and international interest rates. We find that a single-factor general parametric model (1FGPM) of the term structure, with non-linearity in the drift function, better captures the time series dynamics of US 30 Day T-Bill rates. The 1FGPM not only forecasts interest rate changes out-of-sample better relative to other parametric models, but also relative to the non-parametric model of Jiang (1998). Finally, our results vary greatly across international markets. Building upon the work of Longstaff and Schwartz (1992), we perform a statistical analysis of the U.S. default-free term structure over the period 4:1964 to 10:1997. We utilize a constant correlation multivariate GARCH principal components analysis (CCM-PCA), and identify at least three factors associated with traditional measures of risk in the fixed income literature (level, slope, and curvature) that capture 98% of the variation in the default-free term structure. We perform tests of various term structure models on US Treasury bonds, comparing a two factor Cox-Ingersoll-Ross (2FCIR) model with a multi-layer perceptron neural network approach (MLP-ANN), in pricing and hedging discount bonds. We find that while the MLP-ANN can better fit bond prices in-sample, the 2F-CIR model is superior in hedging against unanticipated changes in the short rate and its volatility. Furthermore, we find the 2FCIR model to perform favorably in comparison to the CCM-PCA, MLP-ANN, as well as the 1FGPM in forecasting bond yield changes. Finally, we compare various interest rate bond option pricing models, in their ability to price interest rate derivatives and manage and interest rate risk. We compare three approaches to pricing interest rate derivatives: spot rate (e.g., CIR), forward-rate (i.e., HJM), and non-parametric models (e.g., multivariate kernel estimation.) This is extended to a broader factor structure. While the best model in terms of mean square error (MSE) is the non parametric (MNWK) model, the 3 factor jump diffusion (3FGJD) model performs best among parametric models. In hedging analysis, while these preferred models still outperform within each grouping, the non parametric model is no longer the best performing model, while the 2FCIR is the best model in hedging options in terms of MSE.
Volatility
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Author : Robert A. Jarrow
language : en
Publisher:
Release Date : 1998
Volatility written by Robert A. Jarrow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Derivative securities categories.
Written by a number of authors, this text is aimed at market practitioners and applies the latest stochastic volatility research findings to the analysis of stock prices. It includes commentary and analysis based on real-life situations.
Risk Neutral Valuation
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Author : Nicholas H. Bingham
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Risk Neutral Valuation written by Nicholas H. Bingham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This second edition - completely up to date with new exercises - provides a comprehensive and self-contained treatment of the probabilistic theory behind the risk-neutral valuation principle and its application to the pricing and hedging of financial derivatives. On the probabilistic side, both discrete- and continuous-time stochastic processes are treated, with special emphasis on martingale theory, stochastic integration and change-of-measure techniques. Based on firm probabilistic foundations, general properties of discrete- and continuous-time financial market models are discussed.
Complex Systems In Finance And Econometrics
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-03
Complex Systems In Finance And Econometrics written by Robert A. Meyers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-03 with Business & Economics categories.
Finance, Econometrics and System Dynamics presents an overview of the concepts and tools for analyzing complex systems in a wide range of fields. The text integrates complexity with deterministic equations and concepts from real world examples, and appeals to a broad audience.
The Journal Of Derivatives
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Author :
language : en
Publisher:
Release Date : 2002
The Journal Of Derivatives written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Derivative securities categories.