Related papers: A structural approach to default modelling with pu…
We price and replicate a variety of claims written on the log price $X$ and quadratic variation $[X]$ of a risky asset, modeled as a positive semimartingale, subject to stochastic volatility and jumps. The pricing and hedging formulas do…
During the last decade Levy processes with jumps have received increasing popularity for modelling market behaviour for both derviative pricing and risk management purposes. Chan et al. (2009) introduced the use of empirical likelihood…
We develop a stochastic macro-financial model in continuous time by integrating two specifications of the Keen economic framework with a financial market driven by a jump-diffusion process. The economic block of the model combines monetary…
This paper provides an alternative approach to Duffie and Lando [Econometrica 69 (2001) 633-664] for obtaining a reduced form credit risk model from a structural model. Duffie and Lando obtain a reduced form model by constructing an economy…
We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite…
Filiz et al. (2008) proposed a model for the pattern of defaults seen among a group of firms at the end of a given time period. The ingredients in the model are a graph, where the vertices correspond to the firms and the edges describe the…
We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. Each of the element in this sequence…
In banking practice, rating transition matrices have become the standard approach of deriving multi-year probabilities of default (PDs) from one-year PDs, the latter normally being available from Basel ratings. Rating transition matrices…
L\'{e}vy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on L\'{e}vy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse…
We consider a structural model where the survival/default state is observed together with a noisy version of the firm value process. This assumption makes the model more realistic than most of the existing alternatives, but triggers…
We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with pair-copula constructions, and nest…
A direct method for calculating default rates by industry and target corporate segments is not possible given the lack of statistical data. The proposed paper considers a model for filtering the dynamics of the probability of default of…
Under the International Financial Reporting Standards (IFRS) 9, credit losses ought to be recognised timeously and accurately. This requirement belies a certain degree of dynamicity when estimating the constituent parts of a credit loss…
We present the qGaussian generalization of the Merton framework, which takes into account slow fluctuations of the volatility of the firms market value of financial assets. The minimal version of the model depends on the Tsallis entropic…
We discuss utility based pricing and hedging of jump diffusion processes with emphasis on the practical applicability of the framework. We point out two difficulties that seem to limit this applicability, namely drift dependence and…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given…
In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the L\'evy processes and is able to realistically reproduce the jump-type…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…