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We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clustering feature by adding…
In this work we present a general representation formula for the price of a vulnerable European option, and the related CVA in stochastic (either rough or not) volatility models for the underlying's price, when admitting correlation with…
We develop series expansions in powers of $q^{-1}$ and $q^{-1/2}$ of solutions of the equation $\psi(z) = q$, where $\psi(z)$ is the Laplace exponent of a hyperexponential L\'{e}vy process. As a direct consequence we derive analytic…
This paper considers an aggregator of Electric Vehicles (EVs) who aims to learn the aggregate power of his/her fleet while also participating in the electricity market. The proposed approach is based on a data-driven inverse optimization…
In electricity markets, futures contracts typically function as a swap since they deliver the underlying over a period of time. In this paper, we introduce a market price for the delivery periods of electricity swaps, thereby opening an…
We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is…
We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed L\'evy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of…
The paper builds a Variance-Gamma (VG) model with five parameters: location ($\mu$), symmetry ($\delta$), volatility ($\sigma$), shape ($\alpha$), and scale ($\theta$); and studies its application to the pricing of European options. The…
The presence of integer variables in the European day-ahead electricity market renders the social welfare maximization problem non-convex and non-differentiable, making classical marginal pricing theoretically inconsistent. Existing pricing…
In this paper we present a regression based model for day-ahead electricity spot prices. We estimate the considered linear regression model by the lasso estimation method. The lasso approach allows for many possible parameters in the model,…
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative…
In April 2020, the Chicago Mercantile Exchange temporarily switched the pricing formula for West Texas Intermediate oil market options from the Black model to the Bachelier model. In this context, we introduce an additive Bachelier model…
This paper proposes a risk-averse approach to energy storage price arbitrage, leveraging conformal uncertainty quantification for electricity price predictions. The method addresses the significant challenges posed by the inherent…
Semi-analytical pricing of American options in a time-dependent Ornstein-Uhlenbeck model was presented in [Carr, Itkin, 2020]. It was shown that to obtain these prices one needs to solve (numerically) a nonlinear Volterra integral equation…
The European power grid can be divided into several market areas where the price of electricity is determined in a day-ahead auction. Market participants can provide continuous hourly bid curves and combinatorial bids with associated…
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…
Electricity prices in liberalized markets are determined by the supply and demand for electric power, which are in turn driven by various external influences that vary strongly in time. In perfect competition, the merit order principle…