Related papers: L\'evy-Vasicek Models and the Long-Bond Return Pro…

A unified analytical pricing framework with involvement of the shot noise random process has been introduced and elaborated. Two exactly solvable new models have been developed. The first model has been designed to value options. It is…

We derive a generalised It\=o formula for stochastic processes which are constructed by a convolution of a deterministic kernel with a centred L\'evy process. This formula has a unifying character in the sense that it contains the classical…

Motivated by the application to German interest rates, we propose a timevarying autoregressive model for short and long term prediction of time series that exhibit a temporary non-stationary behavior but are assumed to mean revert in the…

This paper proposes a market consistent valuation framework for variable annuities with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based on a hybrid model for the financial market and…

We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient…

One popular approach to option pricing in L\'evy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber…

Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of…

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 develop a general method for derivative pricing. This approach has its roots in Shannon's Information Theory. The notion of $\lambda$-analyticity of L\'{e}vy models is introduced on the basis of which new representations of the pricing…

We construct an estimator of the L\'evy density of a pure jump L\'evy process, possibly of infinite variation, from the discrete observation of one trajectory at high frequency. The novelty of our procedure is that we directly estimate the…

We provide a complete representation of the interest rate in the extended CIR model. Since it was proved in Maghsoodi (1996) that the representation of the CIR process as a sum of squares of independent Ornstein-Uhlenbeck processes is…

The LIBOR Market Model (LMM) is a widely used model for pricing interest rate derivatives. While the Black-Scholes model is well-known for pricing stock derivatives such as stock options, a larger portion of derivatives are based on…

We introduce here for the first time the long-term swap rate, characterised as the fair rate of an overnight indexed swap with infinitely many exchanges. Furthermore we analyse the relationship between the long-term swap rate, the long-term…

We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…

This paper studies the invertibility property of continuous time moving average processes driven by a L\'evy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel…

This paper develops general approaches for pricing various types of American-style Parisian options (down-in/-out, perpetual/finite-maturity) with general payoff functions based on continuous-time Markov chain (CTMC) approximation under…

We propose a novel framework for modeling the yield curve from a quantile perspective. Building on the dynamic Nelson-Siegel model of Diebold et al. (2006), we extend its traditional mean-based approach to a quantile regression setting,…

L\'evy processes are widely used in financial mathematics to model return data. Price processes are then defined as a corresponding geometric L\'evy process, implying the fact that returns are independent. In this paper we propose an…

A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…

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…