Related papers: Rational term structure models with geometric Levy…

We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity…

First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback.…

We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…

We consider a market with a term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results in this direction: first, the random field of forward rates is driven by a general…

Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…

We present a thorough empirical study on real interest rates by also including risk aversion through the introduction of the market price of risk. With the view of complex systems science and its multidisciplinary approach, we use the…

The classical derivation of the well-known Vasicek model for interest rates is reformulated in terms of the associated pricing kernel. An advantage of the pricing kernel method is that it allows one to generalize the construction to the…

The additive process generalizes the L\'evy process by relaxing its assumption of time-homogeneous increments and hence covers a larger family of stochastic processes. Recent research in option pricing shows that modeling the underlying log…

Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from…

This 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…

The objective of the paper is to price weather contracts using temperature as the underlying process when the later follows a mean-reverting dynamics driven by a time-changed Brownian motion coupled to a Gamma Levy subordinator and…

This paper considers options pricing when the assumption of normality is replaced with that of the symmetry of the underlying distribution. Such a market affords many equivalent martingale measures (EMM). However we argue (as in the…

The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In…

This paper focuses on the pricing of the variance swap in an incomplete market where the stochastic interest rate and the price of the stock are respectively driven by Cox-Ingersoll-Ross model and Heston model with simultaneous L\'{e}vy…

This paper gives examples of explicit arbitrage-free term structure models with L\'evy jumps via state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a L\'evy process…

The utility-based pricing of defaultable bonds in the case of stochastic intensity models of default risk is discussed. The Hamilton-Jacobi- Bellman (HJB) equations for the value functions is derived. A finite difference method is used to…

We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models…

Stochastic volatility models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets such as rich autocorrelation structures, persistence and roughness of sample…

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…

We present an overview of the broad class of financial models in which the prices of assets are L\'evy-Ito processes driven by an $n$-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is…