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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 conduct the first rigorous study of electricity price volatility for the full panel of electricity prices across three European generation zones. By interpreting the observed day-ahead prices as local averages of a latent price process…
In this paper, we present analytical proof demonstrating that the Sandwiched Volterra Volatility (SVV) model is able to reproduce the power-law behavior of the at-the-money implied volatility skew, provided the correct choice of the…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit…
In Europe, Germany is taking the lead in the switch from the conventional to renewable energy. This poses new challenges as wind and solar energy are fundamentally intermittent, weather-dependent and less predictable. It is therefore of…
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and…
The spot pricing scheme has been considered to be resource-efficient for providers and cost-effective for consumers in the Cloud market. Nevertheless, unlike the static and straightforward strategies of trading on-demand and reserved Cloud…
Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the…
Several approaches have been proposed to forecast day-ahead locational marginal price (daLMP) in deregulated energy markets. The rise of deep learning has motivated its use in energy price forecasts but most deep learning approaches fail to…
The recent research report of U.S. Department of Energy prompts us to re-examine the pricing theories applied in electricity market design. The theory of spot pricing is the basis of electricity market design in many countries, but it has…
The goal of this paper is to investigate how the marginal and dependence structures of a variety of multivariate L\'evy models affect calibration and pricing. To this aim, we study the approaches of Luciano and Semeraro (2010) and Ballotta…
We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra…
We study a two-dimensional McKean-Vlasov stochastic differential equation, whose volatility coefficient depends on the conditional distribution of the second component with respect to the first component. We prove the strong existence and…
Financial markets are a complex dynamical system. The complexity comes from the interaction between a market and its participants, in other words, the integrated outcome of activities of the entire participants determines the markets trend,…
We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional L\'evy process. We set up a valuation model in…
Our paper aims to model and forecast the electricity price by taking a completely new perspective on the data. It will be the first approach which is able to combine the insights of market structure models with extensive and modern…
We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic…
In industrial applications it is quite common to use stochastic volatility models driven by semi-martingale Markov volatility processes. However, in order to fit exactly market volatilities, these models are usually extended by adding a…
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a…