Exponential moments of affine processes

Keller‐Ressel, Martin; Mayerhofer, Eberhard

doi:10.1214/14-aap1009

Cited by 69 publications

(86 citation statements)

References 33 publications

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“…In this section, we propose a flexible and tractable specification of the general framework of Section 3.3 based on affine processes. Concerning the analytical properties and the full characterization of such Markov processes on different state spaces we refer to [17], [10], and [42]. Throughout this section T denotes a fixed time horizon and we work on a filtered probability space (Ω, F, (F t ) 0≤t≤T , Q), where Q is a risk neutral measure under which OIS bonds and FRA contracts when discounted with the OIS bank account are martingales.…”

Section: 22mentioning

confidence: 99%

A general HJM framework for multiple yield curve modelling

2016

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Abstract. We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is an affine process, we obtain a flexible and tractable Markovian structure. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.

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Section: 22mentioning

confidence: 99%

A general HJM framework for multiple yield curve modelling

2016

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“…3. We finally use the results of Keller-Ressel and Mayerhofer [49] to provide an analytic extension to the complex plane which allows us to employ formula (5.3) to price FX options. The first step is accomplished via the following result.…”

Section: European Fx Optionsmentioning

confidence: 99%

“…It turns out that extending the validity of the affine formulas that we reported above is not a trivial issue. There exists a branch of literature which focuses on the problem of the existence of exponential moments for affine processes; see Filipovic and Mayerhofer [33], Kallsen and Muhle-Karbe [48], Spreij and Veerman [69], Glasserman and Kim [37], and Keller-Ressel and Mayerhofer [49]. It is not a priori clear, for example, whether the transform formula holds for any time horizon T or whether we can legitimately extend the affine formula to general real or complex moments.…”

Section: Regularity Of the Affine Transform Formulamentioning

confidence: 99%

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An Affine Multicurrency Model with Stochastic Volatility and Stochastic Interest Rates

Gnoatto¹,

Grasselli

2014

SIAM J. Finan. Math.

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We introduce a tractable multicurrency model with stochastic volatility and correlated stochastic\ud interest rates that takes into account the smile in the foreign exchange (FX) market and the evolution\ud of yield curves. The pricing of vanilla options on FX rates can be efficiently performed through the\ud FFT methodology thanks to the affine property of the model. Our framework is also able to describe\ud many nontrivial links between FX rates and interest rates: a calibration exercise highlights the ability\ud of the model to simultaneously fit FX implied volatilities while being coherent with interest rate\ud product

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“…Assuming that it is known that the characteristic function is of the form (1.1) (the process is affine), the sequence of steps that one can follow and which is proved in Keller-Ressel and Mayerhofer (2015) [Theorems 2.14, and 2.26] for classes more general than in Duffie, Filipović, and Singleton (2002) is as follows.…”

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confidence: 99%

Pitfalls of the Fourier Transform Method in Affine Models, and Remedies

Levendorskiı̌

2016

Applied Mathematical Finance

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We study sources of potentially serious errors of popular numerical realizations of the Fourier method in affine models and explain that, in many cases, a calibration procedure based on such a realization will be able to find a "correct parameter set" only in a rather small region of the parameter space, with a blind spot: an interval of strikes depending on the model and time to maturity, where accurate calculations are extremely time-consuming. We explain how to construct more accurate and faster pricing and calibration procedures. An important ingredient of our method is the study of the analytic continuation of the solution of the associated system of generalized Riccati equations, and contour deformation techniques. As a byproduct, we show that the straightforward application of the Runge-Kutta method may lead to sizable errors, and suggest certain remedies. In the paper, the method is applied to a wide class of stochastic volatility models with stochastic interest rate and interest rate models of A n (n) class. The methodology of the paper can be applied to other models (e.g., quadratic term structure models, Wishart dynamics, 3/2-model).

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Exponential moments of affine processes

Cited by 69 publications

References 33 publications

A general HJM framework for multiple yield curve modelling

A general HJM framework for multiple yield curve modelling

An Affine Multicurrency Model with Stochastic Volatility and Stochastic Interest Rates

Pitfalls of the Fourier Transform Method in Affine Models, and Remedies

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