计算金融
In this paper, the cross-correlations of cryptocurrency returns are analysed. The paper examines one years worth of data for 146 cryptocurrencies from the period January 1 2019 to December 31 2019. The cross-correlations of these returns…
Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Heston's (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in…
Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting…
We introduce the notion of Point in Time Economic Scenario Generation (PiT ESG) with a clear mathematical problem formulation to unify and compare economic scenario generation approaches conditional on forward looking market data. Such PiT…
We propose an adaptive and explicit fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme to solve the American put options problem. First, the free boundary problem is converted into a system of partial…
The use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives is investigated. The ability to move beyond the class of convex risk measures considered in…
We consider the numerical approximation of $\mathbb{P}[G\in \Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$…
AI in finance broadly refers to the applications of AI techniques in financial businesses. This area has been lasting for decades with both classic and modern AI techniques applied to increasingly broader areas of finance, economy and…
The rapid development of artificial intelligence methods contributes to their wide applications for forecasting various financial risks in recent years. This study introduces a novel explainable case-based reasoning (CBR) approach without a…
The availability of accurate day-ahead electricity price forecasts is pivotal for electricity market participants. In the context of trade liberalisation and market harmonisation in the European markets, accurate price forecasting becomes…
We use an adversarial expert based online learning algorithm to learn the optimal parameters required to maximise wealth trading zero-cost portfolio strategies. The learning algorithm is used to determine the relative population dynamics of…
We propose a method based on continuous time Markov chain approximation to compute the distribution of Parisian stopping times and price Parisian options under general one-dimensional Markov processes. We prove the convergence of the method…
We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…
Financial markets tend to switch between various market regimes over time, making stationarity-based models unsustainable. We construct a regime-switching model independent of asset classes for risk-adjusted return predictions based on…
Modelling in finance is a challenging task: the data often has complex statistical properties and its inner workings are largely unknown. Deep learning algorithms are making progress in the field of data-driven modelling, but the lack of…
We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature of a principal fibre bundle.…
Through in-depth analysis of ultra high frequency (UHF) stock price change data, more reasonable discrete dynamic distribution models are constructed in this paper. Firstly, we classify the price changes into several categories. Then,…
Consistent Recalibration models (CRC) have been introduced to capture in necessary generality the dynamic features of term structures of derivatives' prices. Several approaches have been suggested to tackle this problem, but all of them,…
The computation of Greeks is a fundamental task for risk managing of financial instruments. The standard approach to their numerical evaluation is via finite differences. Most exotic derivatives are priced via Monte Carlo simulation: in…
There is no exact closed form formula for pricing of European options with discrete cash dividends under the model where the underlying asset price follows a piecewise lognormal process with jumps at dividend ex-dates. This paper presents…