A note on the valuation of CDS options and extension risk in a structural model with jumps

2016 ◽  
Vol 03 (02) ◽  
pp. 1650011
Author(s):  
Amelie Hüttner ◽  
Matthias Scherer
Keyword(s):  
Monte Carlo ◽  
Capital Structure ◽  
Structural Model ◽  
Structural Models ◽  
Jump Diffusion ◽  
Monte Carlo Algorithm ◽  
Default Model ◽  
Brownian Bridges

We consider the valuation of single name CDS options (CDSO) and related optionalities, particularly extension risk, in the structural default model introduced by Chen and Kou (2009). This jump-diffusion based model is able to generate realistic dynamics for CDS spreads and has decent calibration performance. Due to the European character of the considered options, they can be valued with an efficient Monte Carlo algorithm based on Brownian bridges, adapted from Ruf and Scherer (2011). In contrast to the intensity approach, structural models offer a link to the equity side of a firm’s capital structure, possibly enabling to hedge CDS options with instruments other than CDS.

scholarly journals A Novel Hybrid Monte Carlo Algorithm for Sampling Path Space

2021 ◽  
Author(s):  
Francis J. Pinski
Keyword(s):  
Monte Carlo ◽  
Phase Space ◽  
Mass Operator ◽  
Computer Experiments ◽  
Two Dimensions ◽  
Path Space ◽  
Monte Carlo Algorithm ◽  
Hamiltonian Flow ◽  
Hybrid Monte Carlo ◽  
Brownian Bridges

To sample from complex, high-dimensional distributions, one may choose algorithms based on the Hybrid Monte Carlo (HMC) method. HMC-based algorithms generate nonlocal moves alleviating diffusive behavior. Here, I build on an already defined HMC framework, Hybrid Monte Carlo on Hilbert spaces [A. Beskos, F.J. Pinski, J.-M. Sanz-Serna and A.M. Stuart, Stoch. Proc. Applic. 121, 2201 - 2230 (2011); doi:10.1016/j.spa.2011.06.003] that provides finite-dimensional approximations of measures π which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert (path) space. In all HMC algorithms, one has some freedom to choose the mass operator. The novel feature of the algorithm described in this article lies in the choice of this operator. This new choice defines a Markov Chain Monte Carlo (MCMC) method which is well defined on the Hilbert space itself. As before, the algorithm described herein uses an enlarged phase space Π having the target π as a marginal, together with a Hamiltonian flow that preserves Π. In the previous method, the phase space π was augmented with Brownian bridges. With the new choice for the mass operator, π is augmented with Ornstein-Uhlenbeck (OU) bridges. The covariance of Brownian bridges grows with its length, which has negative effects on the Metropolis-Hasting acceptance rate. This contrasts with the covariance of OU bridges which is independent of the path length. The ingredients of the new algorithm include the definition of the mass operator, the equations for the Hamiltonian flow, the (approximate) numerical integration of the evolution equations, and finally the Metropolis-Hastings acceptance rule. Taken together, these constitute a robust method for sampling the target distribution in an almost dimension-free manner. The behavior of this novel algorithm is demonstrated by computer experiments for a particle moving in two dimensions, between two free-energy basins separated by an entropic barrier.

scholarly journals A Novel Hybrid Monte Carlo Algorithm for Sampling Path Space

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 499
Author(s):  
Francis J. Pinski
Keyword(s):  
Monte Carlo ◽  
Phase Space ◽  
Mass Operator ◽  
Computer Experiments ◽  
Path Space ◽  
Monte Carlo Algorithm ◽  
Hamiltonian Flow ◽  
Mcmc Method ◽  
Hybrid Monte Carlo ◽  
Brownian Bridges

To sample from complex, high-dimensional distributions, one may choose algorithms based on the Hybrid Monte Carlo (HMC) method. HMC-based algorithms generate nonlocal moves alleviating diffusive behavior. Here, I build on an already defined HMC framework, hybrid Monte Carlo on Hilbert spaces (Beskos, et al. Stoch. Proc. Applic. 2011), that provides finite-dimensional approximations of measures π, which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert (path) space. In all HMC algorithms, one has some freedom to choose the mass operator. The novel feature of the algorithm described in this article lies in the choice of this operator. This new choice defines a Markov Chain Monte Carlo (MCMC) method that is well defined on the Hilbert space itself. As before, the algorithm described herein uses an enlarged phase space Π having the target π as a marginal, together with a Hamiltonian flow that preserves Π. In the previous work, the authors explored a method where the phase space π was augmented with Brownian bridges. With this new choice, π is augmented by Ornstein–Uhlenbeck (OU) bridges. The covariance of Brownian bridges grows with its length, which has negative effects on the acceptance rate in the MCMC method. This contrasts with the covariance of OU bridges, which is independent of the path length. The ingredients of the new algorithm include the definition of the mass operator, the equations for the Hamiltonian flow, the (approximate) numerical integration of the evolution equations, and finally, the Metropolis–Hastings acceptance rule. Taken together, these constitute a robust method for sampling the target distribution in an almost dimension-free manner. The behavior of this novel algorithm is demonstrated by computer experiments for a particle moving in two dimensions, between two free-energy basins separated by an entropic barrier.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

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