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In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…
In this paper we consider several continuous-time multivariate non-Gaussian models applied to finance and proposed in the literature in the last years. We study the models focusing on the parsimony of the number of parameters, the…
In dynamical framework the conflict between government and the central bank according to the exchange Rate of payment of fixed rates and fixed rates of fixed income (EMU) convergence criteria such that the public debt / GDP ratio The method…
We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an…
We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar L\'evy-type stochastic processes. We derive rigorous error bounds for the…
The trading ecosystem of the Municipal (muni) bond is complex and unique. With nearly 2\% of securities from over a million securities outstanding trading daily, determining the value or relative value of a bond among its peers is…
We consider the supOU stochastic volatility model which is able to exhibit long-range dependence. For this model we give conditions for the discounted stock price to be a martingale, calculate the characteristic function, give a strip where…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The…
We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of…
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential L\'evy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent L\'evy measure.…
In traditional financial markets, yield curves are widely available for countries (and, by extension, currencies), financial institutions, and large corporates. These curves are used to calibrate stochastic interest rate models, discount…
This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent…
Option pricing formulas are derived from a non-Gaussian model of stock returns. Fluctuations are assumed to evolve according to a nonlinear Fokker-Planck equation which maximizes the Tsallis nonextensive entropy of index $q$. A generalized…
To construct a no-arbitrage defaultable bond market, we work on the state price density framework. Using the heat kernel approach (HKA for short) with the killing of a Markov process, we construct a single defaultable bond market that…
In this study we consider the pricing of energy derivatives when the evolution of spot prices is modeled with a normal tempered stable driven Ornstein-Uhlenbeck process. Such processes are the generalization of normal inverse Gaussian…
The problem of European-style option pricing in time-changed L\'{e}vy models in the presence of compound Poisson jumps is considered. These jumps relate to sudden large drops in stock prices induced by political or economical hits. As the…
We study the pricing and the hedging of claim {\psi} which depends on the default times of two firms A and B. In fact, we assume that, in the market, we can not buy or sell any defaultable bond of the firm B but we can only trade…
In this article we propose a $\alpha$-hypergeometric model with uncertain volatility (UV) where we derive a worst-case scenario for option pricing. The approach is based on the connexion between a certain class of nonlinear partial…
The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian…