A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Improved options pricing for two assets using fractional calculus.
The paper derives market-based correlations between asset prices and returns.
This article presents a finite element method (FEM) for a partial integro-differential equation (PIDE) to price two-asset options with underlying price processes modeled by an exponential Levy process. We provide a variational formulation in a weighted Sobolev space, and establish existence and uniqueness of the FEM-ba…
The paper efficiently solves a complex option valuation equation for two assets.
Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of , or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bo…
The paper develops and tests operator splitting schemes for American options in a complex model.
Investigates price dynamics of two assets with and without bubbles, deriving conditions for equilibrium prices.
The aim of this paper is to compare two asset allocation methods for a pension scheme during the decumulation phase in the simplified portfolio selection between a risky asset following a geometric Brownian motion and a riskless asset. The two asset allocation criteria are the ruin probability of the insurance company …
Method extends option valuation for 2D Lévy models.
This paper develops a novel numerical method for pricing American options in a two-asset jump-diffusion model.
An explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utility. We assume a complete market with a finite number of assets and a finite number of possible outcomes. Explicit calculations are performed…
We introduce a new Self-Organized Criticality (SOC) model for simulating price evolution in an artificial financial market, based on a multilayer network of traders. The model also implements, in a quite realistic way with respect to previous studies, the order book dy- namics, by considering two assets with variable f…
We present a simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us…
Optimal design of automated market makers for decentralized exchanges.
We extend to the multi-asset case the framework of a discrete time model of a single asset financial market developed in Ghoulmie et al (2005). In particular, we focus on adaptive agents with threshold behavior allocating their resources among two assets. We explore numerically the effect of this diversification as an …
In this paper we study mean-variance hedging under the G-expectation framework. Our analysis is carried out by exploiting the G-martingale representation theorem and the related probabilistic tools, in a contin- uous financial market with two assets, where the discounted risky one is modeled as a symmetric G-martingale…
Covered bonds are a specific example of senior secured debt. If the issuer of the bonds defaults the proceeds of the assets in the cover pool are used for their debt service. If in this situation the cover pool proceeds do not suffice for the debt service, the creditors of the bonds have recourse to the issuer's assets…
We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of the graph of the option price, related to our strategy, demonstrates the "skewness…
Based on a recent theorem due to the authors, it is shown how the extreme tail dependence between an asset and a factor or index or between two assets can be easily calibrated. Portfolios constructed with stocks with minimal tail dependence with the market exhibit a remarkable degree of decorrelation with the market at…
CFMMs solve complex multi-asset trades via convex optimization.
Develops a new method for online conformal prediction without manual tuning.
We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend ou…
This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments the temporal convergence behaviour of three modern splitting methods: the explic…
The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff funct…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct maturities and the no-arbitrage condition, but without any assumption on the pric…
We introduce a new non parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this method by applying it to high-frequency order book data from the EUREX exchange. We…
New method calibrates MQHawkes model using non-parametric approach, identifying cross-Hawkes and cross-leverage effects.
A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely applied investment strategy in the financial industry. Recently, Ekström, Lindberg and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is…
New formula for efficient spread option pricing in copula markets.
In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of financial derivatives. We present a significantly improved RBF-FD scheme and successfull…
Predicting the price correlation of two assets for future time periods is important in portfolio optimization. We apply LSTM recurrent neural networks (RNN) in predicting the stock price correlation coefficient of two individual stocks. RNNs are competent in understanding temporal dependencies. The use of LSTM cells fu…
We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra processes are in general not semimart…
We unify and extend a number of approaches related to constructing multivariate Variance-Gamma (V.G.) models for option pricing. An overarching model is derived by subordinating multivariate Brownian motion to a subordinator from the Thorin (1977) class of generalised Gamma convolution subordinators. A class of models …
In this paper we study recent developments in the approximation of the spread option pricing. As the Kirkś Approximation is extremely flawed in the cases when the correlation is very high, we explore a recent development that allows approximating with simplicity and accuracy the option price. To assess the goodness of …
Study optimizes investment strategies in volatile markets using machine learning and Bayesian techniques.
Paper reduces dimensionality for robust option pricing in 2-asset markets.
We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which rational investors and noise traders co-exist. Rational investors form expectations on the return and risk of a risky asset and maximize their constant relative risk aversion expected utility with respect to thei…
We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market in terms of contiguity properties of sequences of equivalent probability measures induced by $\la_n$--consistent p…
Deep learning models improve stock market portfolio returns.
With the recent rise of Machine Learning as a candidate to partially replace classic Financial Mathematics methodologies, we investigate the performances of both in solving the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two assets that are intertwined. In Fin…
The value of an asset in a financial market is given in terms of another asset known as numeraire. The dynamics of the value is non-stationary and hence, to quantify the relationships between different assets, one requires convenient measures such as the means and covariances of the respective log returns. Here, we dev…
Modeling fees impacts on arbitrage profits and LP losses in AMMs.
We consider a portfolio allocation problem for trend following (TF) strategies on multiple correlated assets. Under simplifying assumptions of a Gaussian market and linear TF strategies, we derive analytical formulas for the mean and variance of the portfolio return. We construct then the optimal portfolio that maximiz…
The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most frequently in Financial and Actuarial Mathematics.) In this note we discuss short …
We propose a modelling framework for the optimal selection of crypto assets. Crypto assets differ by two essential features: security (technological) and stability (governance). Investors make choices over crypto assets similarly to how they make choices by using a recommender app: the app presents each investor with a…
The paper develops Hawkes-based models for LOB and applies them to European, spread, and basket option pricing.
No fair and strategy-proof automated market maker exists for more than two assets.
Maximizes probability of completing investment schedules with optimal portfolio weights.