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This paper introduces the class of volatility modulated L\'{e}vy-driven Volterra (VMLV) processes and their important subclass of L\'{e}vy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main…
A Levy-driven Ornstein-Uhlenbeck process is proposed to model the evolution of the risk-free rate and default intensities for the purpose of evaluating option contracts on a credit index. Time evolution in credit markets is assumed to…
In this paper we compare two classical one-factor diffusion models which are used to model the term structure of interest rates. One of them is based on the Wiener-Bachelier process while the second one is based on the Ornstein-Uhlenbeck…
A core challenge in causal inference is how to extrapolate long term effects, of possibly continuous actions, from short term experimental data. It arises in artificial intelligence: the long term consequences of continuous actions may be…
We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial…
We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential L\'evy model driven by the Normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric model, and…
Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around $\mathbb{R}\subset \mathbb{C}$. The Fourier transform techniques reduces calculation…
In this paper we formulate a corporate bond (CB) pricing model for deriving the term structure of default probabilities (TSDP) and the recovery rate (RR) for each pair of industry factor and credit rating grade, and these derived TSDP and…
This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms. First observed in the deep learning literature, we show that…
This paper describes a general approach for stochastic modeling of assets returns and liability cash-flows of a typical pensions insurer. On the asset side, we model the investment returns on equities and various classes of fixed-income…
Guyon and Lekeufack recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylized facts. The instantaneous volatility is modeled as a linear combination of two…
We propose an innovative data-driven option pricing methodology that relies exclusively on the dataset of historical underlying asset prices. While the dataset is rooted in the objective world, option prices are commonly expressed as…
It is well documented from various empirical studies that the volatility process of an asset price dynamics is stochastic. This phenomenon called for a new approach to describing the random evolution of volatility through time with…
The aim of this thesis is to analyze and renovate few main-stream models on inflation derivatives. In the first chapter of the thesis, concepts of financial instruments and fundamental terms are introduced, such as coupon bond,…
We introduce and establish the main properties of QHawkes ("Quadratic" Hawkes) models. QHawkes models generalize the Hawkes price models introduced in E. Bacry et al. (2014), by allowing all feedback effects in the jump intensity that are…
Electricity price is a key factor affecting the decision-making for all market participants. Accurate forecasting of electricity prices is very important and is also very challenging since electricity price is highly volatile due to various…
With $P_t$ the price in current dollars of a dollar delivered $t$ time units from now, we assume that $P$ is a decreasing function defined for $t \in \mathbb{R}_+$ with $P_0 = 1$. The negative logarithmic derivative, $-…
Interactions among multiple time series of positive random variables are crucial in diverse financial applications, from spillover effects to volatility interdependence. A popular model in this setting is the vector Multiplicative Error…
In mathematical finance, Levy processes are widely used for their ability to model both continuous variation and abrupt, discontinuous jumps. These jumps are practically relevant, so reliable inference on the feature that controls jump…
In this article, the problem of semi-parametric inference on the parameters of a multidimensional L\'{e}vy process $L_t$ with independent components based on the low-frequency observations of the corresponding time-changed L\'{e}vy process…