Unspanned Stochastic Volatility in the Multi-Factor CIR Model PDF Download

Author: Damir Filipovic
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Jaya P. N. Bishwal
Publisher: Springer Nature
ISBN: 3031038614
Category : Mathematics
Languages : en
Pages : 634

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This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Author: Anders B. Trolle
Publisher:
ISBN:
Category :
Languages : en
Pages : 66

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We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features unspanned stochastic volatility factors, correlation between innovations to forward rates and their volatilities, quasi-analytical prices of zero-coupon bond options, and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finitedimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities.

Author: Don H. Kim
Publisher:
ISBN:
Category : 1996-2008
Languages : en
Pages : 46

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This paper reexamines the issue of unspanned stochastic volatility (USV) in bond markets and the puzzle of poor relative pricing between bonds and bond options. I make a distinction between the "weak USV" and the "strong USV" scenarios, and analyze the evidence for each of them. I argue that the poor bonds/options relative pricing in the extant literature is not necessarily evidence for the strong USV scenario, and show that a maximally flexible 2-factor quadratic-Gaussian model (a non-USV model) estimated without bond options data can capture much of the movement in bond option prices. Dropping the positive-definiteness requirement for nominal interest rates and adopting "regularized" estimations turn out to be important for obtaining sensible results.

Author: Alexandre Antonov
Publisher:
ISBN:
Category :
Languages : en
Pages : 14

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Stochastic volatility models are widely used in interest rate modeling to match the option smiles -- the two most popular are the Heston model and the SABR one. These have been incorporated into arbitrage-free term structure frameworks, Heston-LMM and SABR-LMM respectively.In this paper we consider the CEV model with a general stochastic volatility. Assuming that rate-volatility correlation is zero we are able to obtain an exact integral representation of the option price provided that we have a closed form for a Moment Generating Function of the cumulative stochastic variance or of its inverse. Using this result we derive explicit solutions in terms of two-dimensional integral for both CEV-CIR model (or power generalization of the Heston) and the SABR one. Moreover the results in this paper may be easily extended to any affine process (possibly multi-factor and including jumps) leading to numerous practical applications.

Author: Michail Korniotis
Publisher:
ISBN: 9781109509427
Category :
Languages : en
Pages : 179

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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: Anders B. Trolle
Publisher:
ISBN:
Category :
Languages : en
Pages : 64

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Book Description
We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasi-analytical prices of zero-coupon bond options and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finite-dimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities. The model also performs well in forecasting interest rates and derivatives.

Author: Andrew Lesniewski
Publisher:
ISBN:
Category :
Languages : en
Pages : 30

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We present a stochastic-volatility, short rate term structure model, which extends the classic multi-factor Hull-White model. This model is designed to fit the swaption implied volatility cube and to incorporate the two-curve modeling paradigm. The model exhibits non-Gaussian forward swap rates whose distributions are parameterized across the dimensions of the volatility cube: underlying tenor, option strike and option expiration. To facilitate rapid model calibration, we establish suitable asymptotic expressions for the bond prices. Furthermore, we derive an effective SABR dynamics for each forward swap rate. Finally, we use the mean field approximation to match the effective SABR parameters corresponding to each swaption to the market levels.

Author: Jin-Chuan Duan
Publisher: Springer Science & Business Media
ISBN: 3642172547
Category : Business & Economics
Languages : en
Pages : 791

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Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.

Author: Walker Keener Hughen
Publisher:
ISBN:
Category :
Languages : en
Pages : 208

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