Related papers: Defaultable Bonds via HKA
We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black-Scholes model as well as the constant elasticity of variance (CEV) model as…
The Constant Elasticity of Variance (CEV) model is mathematically presented and then used in a Credit-Equity hybrid framework. Next, we propose extensions to the CEV model with default: firstly by adding a stochastic volatility diffusion…
Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent.…
We introduce a class of short-rate models that exhibit a ``higher for longer'' phenomenon. Specifically, the short-rate is modeled as a general time-homogeneous one-factor Markov diffusion on a finite interval. The lower endpoint is assumed…
In this paper, we consider a discrete time economy where we assume that the short term interest rate follows a quadratic term structure of a regime switching asset process. The possible non-linear structure and the fact that the interest…
In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in various forms. We…
We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables…
We introduce a financial market model featuring a risky asset whose price follows a sticky geometric Brownian motion and a riskless asset that grows with a constant interest rate $r\in \mathbb R $. We prove that this model satisfies No…
We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and…
According to theoretical models of valuing risky corporate securities, risk of default is primary component in overall yield spread. However, sizable empirical literature considers it otherwise by giving more importance to non-default risk…
In this paper, we study a family of stochastic volatility processes; this family features a mean reversion term for the volatility and a double CEV-like exponent that generalizes SABR and Heston's models. We derive approximated closed form…
We consider a model of debt management, where a sovereign state trade some bonds to service the debt with a pool of risk-neutral competitive foreign investors. At each time, the government decides which fraction of the gross domestic…
A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the…
A multi-dimensional extension of the structural default model with firms' values driven by diffusion processes with Marshall-Olkin-inspired correlation structure is presented. Semi-analytical methods for solving the forward calibration…
A negative basis trade enters a long bond position and buys protection on the issuer of the bond through credit default swap (CDS), aiming at arbitrage profit due to the bond-CDS basis. To classic reduced form model theorists, the existence…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
This article describes a case study concerned with modelling the price of wholesale diamonds, as part of a project to develop an online diamond auction platform. The work was extended to exploring how to develop an index that could be used…
We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii)…