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Implied Volatilities for Options on Backward-Looking Term Rates
Hofmann, Karl F. - 2020
We derive valuation formulas for caps and floors on backward-looking term rates in the Black-1976, Bachelier and Hull-White-1-Factor models explicitly regarding valuation in the fixing period, extending and detailing results of [Lyashenko & Mercurio 2019, Henrard 2019, Turfus 2020]. These...
Persistent link: https://www.econbiz.de/10012834974
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The Markov-Switching Jump Diffusion Libor Market Model
Borchert, Lea - 2018
In this paper, we introduce an extension to the LIBOR Market model that is suitable to incorporate both sudden market shocks as well as changes in the overall economic climate into the interest rate dynamics. This is achieved by substituting the simple diffusion process of the original LIBOR...
Persistent link: https://www.econbiz.de/10012938239
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The Term Structure of Implied Volatility in Symmetric Models with Applications to Heston
De Marco, Stefano - 2010
We study the term structure of the implied volatility in a situation where the smile is symmetric. Starting from the result by Tehranchi that a symmetric smile generated by a continuous martingale necessarily comes from a mixture of normal distributions, we derive representation formulae for the...
Persistent link: https://www.econbiz.de/10013142386
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Conditional density models for asset pricing
Filipović, Damir; Hughston, Lane P.; Macrina, Andrea - 2010
We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...
Persistent link: https://www.econbiz.de/10008797695
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Explicit Constructions of Martingales Calibrated to Given Implied Volatility Smiles
Carr, Peter - 2011
The construction of martingales with given marginal distributions at given times is a recurrent problem in financial mathematics. From a theoretical point of view, this problem is well-known as necessary and sufficient conditions for the existence of such martingales have been described....
Persistent link: https://www.econbiz.de/10013132624
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A Supplement to Remark on Local Volatility
Gikhman, Ilya I. - 2011
The concept of the Local Volatility was developed in [1-3]. Later this concept was broadly generalized and extends in particular to cover stochastic local volatility phenomena. A number of companies offer their products which call for more accurate forecast of options pricing and one can check...
Persistent link: https://www.econbiz.de/10013124197
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Asymptotics for Exponential Levy Processes and Their Volatility Smile : Survey and New Results
Andersen, Leif B. G. - 2012
Exponential Lévy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, etc. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes, and the corresponding implied volatility surfaces...
Persistent link: https://www.econbiz.de/10013104402
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Large Deviations for the Extended Heston Model : The Large-Time Case
Jacquier, Antoine (Jack) - 2012
We study here the large-time behavior of all continuous affine stochastic volatility models (in the sense of Keller-Ressel) and deduce a closed-form formula for the large-maturity implied volatility smile. Based on refinements of the Gartner-Ellis theorem on the real line, our proof reveals...
Persistent link: https://www.econbiz.de/10013108705
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An Examination of the Continuous-Time Dynamics of International Volatility Indices Amid the Recent Market Turmoil
Li, Minqiang - 2013
data. We estimate various continuous-time models for different volatility indices with focus on the structure of the drift … specification test. While the results from the parametric specification test advocate strongly for specifying more flexible drift … and diffusion functions, nonlinear drift structure often only adds negligible benefit in terms of the likelihood function …
Persistent link: https://www.econbiz.de/10013082816
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Arbitrage-Free SVI Volatility Surfaces
Gatheral, Jim - 2014
In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility smile in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form...
Persistent link: https://www.econbiz.de/10013066295