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The third moment variation of a financial asset return process is defined by the quadratic covariation between the return and square return processes. The skew and fat tail risk of an underlying asset can be hedged using a third moment…
Exponential L\'evy processes have been used for modelling financial derivatives because of their ability to exhibit many empirical features of markets. Using their multidimensional analogue, a general analytic pricing formula is obtained,…
This study explores the use of Transformer-based models to predict both covariance and semi-covariance matrices for ETF portfolio optimization. Traditional portfolio optimization techniques often rely on static covariance estimates or…
The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…
In this paper we construct a shrinkage estimator of the global minimum variance (GMV) portfolio by a combination of two techniques: Tikhonov regularization and direct shrinkage of portfolio weights. More specifically, we employ a double…
We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about…
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…
We revisit the recently introduced concept of return risk measures (RRMs) and extend it by incorporating risk management via multiple so-called eligible assets. The resulting new class of risk measures, termed multi-asset return risk…
We develop a semi-static framework for the variance-optimal hedging of multi-asset derivatives exposed to correlation and covariance risk. The approach combines continuous-time dynamic trading in the underlying assets with a static…
In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a…
Randomness in financial markets requires modern and robust multivariate models of risk measures. This paper proposes a new approach for modeling multivariate risk measures under Wasserstein barycenters of probability measures supported on…
We derive a feasible criterion for the bias-optimal selection of the tuning parameters involved in estimating the integrated volatility of the spot volatility via the simple realized estimator by Barndorff-Nielsen and Veraart (2009). Our…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
In this paper, we show that the recent integration of statistical models with deep recurrent neural networks provides a new way of formulating volatility (the degree of variation of time series) models that have been widely used in time…
Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a…
The principal portfolios of the standard Capital Asset Pricing Model (CAPM) are analyzed and found to have remarkable hedging and leveraging properties. Principal portfolios implement a recasting of any correlated asset set of N risky…
We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market--calibrated parameters and the remaining risk associated with idiosyncratic…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…