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The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift,…
We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal…
We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum…
This paper is devoted to the pricing of Barrier options by optimal quadratic quantization method. From a known useful representation of the premium of barrier options one deduces an algorithm similar to one used to estimate nonlinear filter…
This paper addresses a novel data science problem, prescriptive price optimization, which derives the optimal price strategy to maximize future profit/revenue on the basis of massive predictive formulas produced by machine learning. The…
In this bachelor thesis, we show how four different machine learning methods (Long Short-Term Memory, Random Forest, Support Vector Machine Regression, and k-Nearest Neighbor) perform compared to already successfully applied trading…
In this paper we analyze a nonlinear Black--Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a function of the underlying…
We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting…
Advanced classification algorithms are being increasingly used in safety-critical applications like health-care, engineering, etc. In such applications, miss-classifications made by ML algorithms can result in substantial financial or…
Continuous value prediction plays a crucial role in industrial-scale recommendation systems, including tasks such as predicting users' watch-time and estimating the gross merchandise value (GMV) in e-commerce transactions. However, it…
Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, {\bf 2}, 415-431, 2002) to include…
Predicting volatility is important for asset predicting, option pricing and hedging strategies because it cannot be directly observed in the financial market. The Black-Scholes option pricing model is one of the most widely used models by…
We consider approximate pricing formulas for European options based on approximating the logarithmic return's density of the underlying by a linear combination of rescaled Hermite polynomials. The resulting models, that can be seen as…
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
This paper proposes a new objective function and quantile regression (QR) algorithm for load forecasting (LF). In LF, the positive forecasting errors often have different economic impact from the negative forecasting errors. Considering…
The accurate valuation of financial derivatives plays a pivotal role in the finance industry. Although closed formulas for pricing are available for certain models and option types, exemplified by the European Call and Put options in the…
We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on $q$-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities…
The true probability of a European call option to achieve positive return is investigated under the Black-Scholes model. It is found that the probability is determined by those market factors appearing in the BS formula, besides the growth…
his paper presents finite element methods for solving numerically the Risk-Adjusted Pricing Methodology (RAPM) Black-Scholes model for option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are…