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We compare two different bilateral counterparty valuation adjustment (BVA) formulas. The first formula is an approximation and is based on subtracting the two unilateral Credit Valuation Adjustment (CVA)'s formulas as seen from the two…
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte…
Monte Carlo integration becomes prohibitively expensive when each sample requires a high-fidelity model evaluation. Multi-fidelity uncertainty quantification methods mitigate this by combining estimators from high- and low-fidelity models,…
In this paper we propose a comparison between the CTRW (Monte Carlo) and Fractional Derivative approaches to the modelling of anomalous diffusion phenomena in the presence of an advection field. Galilei variant and invariant schemes are…
The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the…
We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR…
In this paper, we investigate risk measures such as value at risk (VaR) and the conditional tail expectation (CTE) of the extreme (maximum and minimum) and the aggregate (total) of two dependent risks. In finance, insurance and the other…
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…
We propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the…
Total value adjustment (XVA) is the change in value to be added to the price of a derivative to account for the bilateral default risk and the funding costs. In this paper, we compute such a premium for American basket derivatives whose…
We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In order to quantify the solution uncertainty, we design a…
In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in costs in addition to minimizing a standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk measure that…
Multi-step stock price prediction over a long-term horizon is crucial for forecasting its volatility, allowing financial institutions to price and hedge derivatives, and banks to quantify the risk in their trading books. Additionally, most…
The dynamic hedging theory only makes sense in the setup of one given model, whereas the practice of dynamic hedging is just the opposite, with models fleeing after the data through daily recalibration. This is quite of a quantitative…
The cardinality-constrained mean-variance portfolio problem has garnered significant attention within contemporary finance due to its potential for achieving low risk while effectively managing risks and transaction costs. Instead of…
We show how the cost of funding the collateral in a particular set up can be equal to the Bilateral Valuation Adjustment with the "funded" probability of default, leading to the definition of a Funded Bilateral Valuation Adjustment (FBVA).…
The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD…
The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate solutions via certain Monte Carlo simulations. The main results represent the upper bound of…
Multilevel Monte Carlo (MLMC) reduces the total computational cost of financial option pricing by combining SDE approximations with multiple resolutions. This paper explores a further avenue for reducing cost and improving power efficiency…
In this paper, we propose a neural network-based method for CVA computations of a portfolio of derivatives. In particular, we focus on portfolios consisting of a combination of derivatives, with and without true optionality, \textit{e.g.,}…