SSRN Author: Vadim LinetskyVadim Linetsky SSRN Content
http://www.ssrn.com/author=108286
http://www.ssrn.com/rss/en-usFri, 28 Jul 2017 02:35:46 GMTeditor@ssrn.com (Editor)Fri, 28 Jul 2017 02:35:46 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Long-Term Factorization of Affine Pricing KernelsThis paper constructs and studies the long-term factorization of affine pricing kernels into discounting at the rate of return on the long bond and the martingale component that accomplishes the change of probability measure to the long forward measure. The principal eigenfunction of the affine pricing kernel germane to the long-term factorization is an exponential-affine function of the state vector with the coefficient vector identified with the fixed point of the Riccati ODE. The long bond volatility and the volatility of the martingale component are explicitly identified in terms of this fixed point. A range of examples from the asset pricing literature is provided to illustrate the theory.
http://www.ssrn.com/abstract=2847418
http://www.ssrn.com/1612264.htmlThu, 27 Jul 2017 05:05:45 GMTREVISION: The Long Bond, Long Forward Measure and Long-Term Factorization In Heath-Jarrow-Morton ModelsThis paper proves existence of the long bond, long forward measure and long-term factorization of the stochastic discount factor (SDF) of Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) in Heath-Jarrow-Morton (HJM) models in the function space framework of Filipovic´ (2001). A sufficient condition on the weight in the Hilbert space of forward rate volatility curves is given that ensures existence of the long bond volatility process, the long bond process and the long-term factorization of the SDF into discounting at the rate of return on the long bond and a martingale component defining the long forward measure, the long-term limit of T-forward measures.
http://www.ssrn.com/abstract=2847417
http://www.ssrn.com/1612263.htmlThu, 27 Jul 2017 05:04:23 GMTNew: (Online Appendix) Marshall-Olkin Distributions, Subordinators, Efficient Simulation, and Applications to Credit RiskThis document contains complementary material of section 6 of the article <i>"Marshall-Olkin Distributions, Subordinators, Efficient Simulation, and Applications to Credit Risk"</i>. In particular, we provide the time-inhomogeneous extensions of Theorems 4.1 and 4.2 of the main document. These results are given in Theorems A.1 and A.2 where Levy subordinators are replaced with additive subordinators. We also present additional extensions to the MO distribution which incorporate stochastic dynamics and extend the traditional default intensity factor model.
<a href='http://ssrn.com/abstract=1702087'>http://ssrn.com/abstract=1702087</a>
http://www.ssrn.com/abstract=2879980
http://www.ssrn.com/1549341.htmlWed, 07 Dec 2016 09:48:39 GMTREVISION: Marshall-Olkin Distributions, Subordinators, Efficient Simulation, and Applications to Credit RiskThe paper presents a novel construction of Marshall-Olkin (MO) multivariate exponential distributions of failure times as distributions of the first passage times of the coordinates of multidimensional Levy subordinator processes above independent unit-mean exponential random variables. A time-inhomogeneous version is also given that replaces Levy subordinators with additive subordinators. An attractive feature of MO distributions for applications, such as to portfolio credit risk, is its singular component that yields positive probabilities of simultaneous defaults of multiple obligors, capturing the default clustering phenomenon. The drawback of the original MO fatal shock construction of MO distributions is that it requires one to simulate <i>2<sup>n</sup>-1</i> independent exponential random variables. In practice, the dimensionality is typically on the order of hundreds or thousands of obligors in a large credit portfolio, rendering the MO fatal shock construction infeasible to ...
http://www.ssrn.com/abstract=1702087
http://www.ssrn.com/1548525.htmlSun, 04 Dec 2016 08:37:26 GMTREVISION: Long-Term Factorization of Affine Pricing KernelsThis paper constructs and studies the long-term factorization of affine pricing kernels into discounting at the rate of return on the long bond and the martingale component that accomplishes the change of probability measure to the long forward measure. The principal eigenfunction of the affine pricing kernel germane to the long-term factorization is an exponential-affine function of the state vector with the coefficient vector identified with the fixed point of the Riccati ODE. The long bond volatility and the volatility of the martingale component are explicitly identified in terms of this fixed point. A range of examples from the asset pricing literature is provided to illustrate the theory.
http://www.ssrn.com/abstract=2847418
http://www.ssrn.com/1533596.htmlThu, 06 Oct 2016 13:54:12 GMTREVISION: Long Term Risk: A Martingale ApproachThis paper extends the long-term factorization of the stochastic discount factor introduced and studied by Alvarez and Jermann (2005) in discrete-time ergodic environments and by Hansen and Scheinkman (2009) and Hansen (2012) in Markovian environments to general semimartingale environments. The transitory component discounts at the stochastic rate of return on the long bond and is factorized into discounting at the long-term yield and a positive semimartingale that extends the principal eigenfunction of Hansen and Scheinkman (2009) to the semimartingale setting. The permanent component is a martingale that accomplishes a change of probabilities to the long forward measure, the limit of T-forward measures. The change of probabilities from the data generating to the long forward measure absorbs the long-term risk-return trade-off and interprets the latter as the long-term risk-neutral measure.
http://www.ssrn.com/abstract=2523110
http://www.ssrn.com/1533378.htmlWed, 05 Oct 2016 22:31:31 GMTREVISION: The Long Bond, Long Forward Measure and Long-Term Factorization In Heath-Jarrow Morton ModelsThis paper proves existence of the long bond, long forward measure and long-term factorization of the stochastic discount factor (SDF) of Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) in Heath-Jarrow-Morton (HJM) models in the function space framework of Filipovi´c (2001). In particular, a sufficient condition on the weight in the Hilbert space of forward rate volatility curves is given that ensures existence of the long bond volatility process, the long bond process and the long-term factorization of the SDF into discounting at the rate of return on the long bond and a martingale component defining the long forward measure, the long-term limit of T-forward measures.
http://www.ssrn.com/abstract=2847417
http://www.ssrn.com/1533067.htmlTue, 04 Oct 2016 18:23:06 GMTREVISION: Long Term Risk: A Martingale ApproachThis paper extends the long-term factorization of the stochastic discount factor introduced and studied by Alvarez and Jermann (2005) in discretetime ergodic environments and by Hansen and Scheinkman (2009) and Hansen(2012) in Markovian environments to general semimartingale environments. The transitory component discounts at the stochastic rate of return on the long bond and is factorized into discounting at the long-term yield and a positive semimartingale that extends the principal eigenfunction of Hansen and Scheinkman (2009) to the semimartingale setting. The permanent component is a martingale that accomplishes a change of probabilities to the long forward measure, the limit of T-forward measures. The change of probabilities from the data generating to the long forward measure absorbs the long-term risk-return trade-off and interprets the latter as the long-term risk-neutral measure.
http://www.ssrn.com/abstract=2523110
http://www.ssrn.com/1521078.htmlFri, 19 Aug 2016 15:42:32 GMT