Linear Credit Risk Models

Ackerer, Damien; Filipović, Damir

doi:10.2139/ssrn.2782455

Cited by 14 publications

(13 citation statements)

References 53 publications

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“…The model proposed in this paper also shares some similarities with the linear hypercube model model of Ackerer and Filipović (2019) in the context of credit risk. Specifically, they specify a survival process whose drift is a linear function of a diffusive factor process with linear drift.…”

Section: Introductionmentioning

confidence: 84%

“…In our setup, the dividend rate is a linear function of a diffusive factor process with linear drift, which has to be specified such that the stock price is positive and the dividend rate non-negative. The stock price, whose drift is linear in the dividend rate, therefore plays a similar role as the survival process in Ackerer and Filipović (2019), but with the important difference that the stock price has a martingale part while the survival process is absolutely continuous. This martingale part requires special care and, in particular, rules out the factor process specification of the linear hypercube model of Ackerer and Filipović (2019).…”

Section: Introductionmentioning

confidence: 99%

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Linear Stochastic Dividend Model

Willems

2019

SSRN Journal

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In this paper we propose a new model for pricing stock and dividend derivatives. We jointly specify dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate non-negative. In its simplest form, the model features a dividend rate that is mean-reverting around a constant fraction of the stock price. The advantage of directly specifying dynamics for the dividend rate, as opposed to the more common approach of modeling the dividend yield, is that it is easier to keep the distribution of cumulative dividends tractable. The model is non-affine but does belong to the more general class of polynomial processes, which allows us to compute all conditional moments of the stock price and the cumulative dividends explicitly. In particular, we have closed-form expressions for the prices of stock and dividend futures. Prices of stock and dividend options are accurately approximated using a moment matching technique based on the principle of maximal entropy. * EPFL and Swiss Finance Institute. 1 In reality, dividends are paid out discretely instead of continuously. Most liquid dividend derivatives, however, reference dividends paid by a stock index, in which case continuously paid dividends are considered an acceptable approximation.

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Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Linear Stochastic Dividend Model

Willems

2019

SSRN Journal

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“…11 In the more general polynomial framework described in Section 2, it is possible to lower bound the short rate. For example, one can use compactly supported polynomial processes, similarly as in Ackerer and Filipović (2020). 12 For a constant > 0, the dynamics of (̃0 ,̃1 ) = ( 0 , 1 ) is given by…”

Section: E N D N O T E Smentioning

confidence: 99%

A term structure model for dividends and interest rates

Filipović

Willems

2020

Mathematical Finance

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Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump‐diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. We present an efficient moment based approximation method for option pricing. In a calibration exercise we show that a parsimonious model specification has a good fit with Euribor interest rate swaps and swaptions, Euro Stoxx 50 Index dividend futures and dividend options, and Euro Stoxx 50 Index options.

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“…Because of their inherent tractability, polynomial jump diffusions have played a prominent and growing role in a wide range of applications in finance. Examples include interest rates (Delbaen and Shirakawa 2002, Zhou 2003, Filipović et al 2017, stochastic volatility (Gourieroux andJasiak 2006, Ackerer et al 2018), exchange rates (Larsen and Sørensen 2007), life insurance liabilities (Biagini and Zhang 2016), variance swaps , credit risk (Ackerer and Filipović 2020a), dividend futures (Filipović and Willems 2019), commodities and electricity (Filipović et al 2018), stochastic portfolio theory (Cuchiero 2019), and economic equilibrium (Guasoni and Wong 2018). Properties of polynomial jump diffusions can also be brought to bear on computational and statistical methods, such as generalized method of moments and martingale estimating functions (Forman and Sørensen 2008), variance reduction (Cuchiero et al 2012), cubature , and quantization (Callegaro et al 2017).…”

Section: Introductionmentioning

confidence: 99%

Polynomial Jump-Diffusion Models

Filipović

Larsson

2020

Stochastic Systems

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We develop a comprehensive mathematical framework for polynomial jump diffusions in a semimartingale context, which nest affine jump diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial transformations and Lévy time change. We present a generic method for option pricing based on moment expansions. As an application, we introduce a large class of novel financial asset pricing models with excess log returns that are conditional Lévy based on polynomial jump diffusions. History: Former designation of this paper was SSy-2019-001.R1.

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Linear Credit Risk Models

Cited by 14 publications

References 53 publications

Linear Stochastic Dividend Model

Linear Stochastic Dividend Model

A term structure model for dividends and interest rates

Polynomial Jump-Diffusion Models

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