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Author: Mark S. Joshi Publisher: ISBN: Category : Languages : en Pages : 25
Book Description
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.
Author: Mark S. Joshi Publisher: ISBN: Category : Languages : en Pages : 25
Book Description
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.
Author: Yacine Aït-Sahalia Publisher: ISBN: Category : Derivative securities Languages : en Pages : 39
Book Description
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.
Author: Yacine Ait-Sahalia Publisher: ISBN: Category : Languages : en Pages : 45
Book Description
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.
Author: Benjamin Cheng Publisher: ISBN: Category : Languages : en Pages : 30
Book Description
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.
Author: Michael Jacobs Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Nicholas H. Bingham Publisher: Springer Science & Business Media ISBN: 1447136195 Category : Mathematics Languages : en Pages : 306
Book Description
With a simple approach accessible to a wide audience, this book aims for the heart of mathematical finance: the fundamental formula of arbitrage pricing theory. This method of pricing discounts everything and takes expected values under the equivalent martingale measure. The authors approach is simple and excludes unnecessary proofs of measure-theoretic probability, instead, it favors techniques and examples of proven interest to financial practitioners.
Author: Alexander van Haastrecht Publisher: ISBN: Category : Languages : en Pages : 28
Book Description
In this paper we extend the stochastic volatility model of Schouml;bel and Zhu (1999) by including stochastic interest rates. Furthermore we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a correlation between the instantaneous interest rates, the volatilities and the underlying stock returns. By deriving the characteristic function of the log-asset price distribution, we are able to price European stock options in closed-form by Fourier inversion. Furthermore we present a Foreign Exchange generalization and show how the pricing of Forward-starting options like cliquets can be performed. Additionally we discuss the practical implementation of these new models.
Author: João Pedro Vidal Nunes Publisher: ISBN: Category : Languages : en Pages :
Book Description
Simple analytical pricing formulae have been derived, by different authors and for several interest rate contingent claims, under the Gaussian Langetieg (1980) model. The purpose of this paper is to use such exact Gaussian solutions in order to obtain approximate analytical pricing formulae under the most general stochastic volatility specification of the Duffie and Kan (1996) model, for several European-style interest rate derivatives, namely for: default-free bonds, FRAs, IRSs, short-term and long-term interest rate futures, European spot and futures options on zero-coupon bonds, interest rate caps and floors, European (conventional and pure) futures options on short-term interest rates, and even for European swaptions. First, the functional form of an Arrow-Debreu price, under the Gaussian specification of the Duffie and Kan (1996) model, is obtained in a slightly more general form than the one given by Beaglehole and Tenney (1991). Then, and following Chen (1996), each stochastic volatility pricing solution is expressed in terms of one integral with respect to each one of the model's state variables, and another integral with respect to the time-to-maturity of the contingent claim under valuation. Finally, unlike in Chen (1996) and as the original contribution of this paper, all stochastic volatility closed form solutions are simplified into first order approximate pricing formulae that do not involve any integration with respect to the model's factors: only one time-integral is involved, irrespective of the model dimension. Consequently, such approximations will be shown to be much faster than the existing exact numerical solutions, as well as accurate. Moreover, asymptotic error bounds are provided for the proposed approximations.
Author: Mark S. Joshi
Author: Mark S. Joshi
Author: Yacine Aït-Sahalia
Author: Yacine Ait-Sahalia
Author: Benjamin Cheng
Author: Antoine Petrus Cornelius van der Ploeg
Author: Michael Jacobs
Author: Nicholas H. Bingham
Author: Alexander van Haastrecht
Author: 
Author: João Pedro Vidal Nunes