数理金融

The stochastic volatility inspired (SVI) model is widely used to fit the implied variance smile. Presently, most optimizer algorithms for the SVI model have a strong dependence on the input starting point. In this study, we develop an…

The purpose of this paper is to utilize statistical methodologies to infer from market prices of assets and their derivatives the magnitude of the set of a measure M that defines acceptance sets of risky future cash flows. Specifically, we…

We consider a discrete-time incomplete multi-asset market model with continuous price jumps. For a wide class of contingent claims, including European basket call options, we compute the bounds of the interval containing the no-arbitrage…

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…

We extend the short rate model of Turfus and Romero-Berm\'udez [2021] to facilitate accurate arbitrage-free analytic pricing of SOFR, SONIA or ESTR caplets, i.e. options on backward-looking compounded rates payments, in a manner consistent…

This article clarifies the relationship between pricing kernel monotonicity and the existence of opportunities for stochastic arbitrage in a complete and frictionless market of derivative securities written on a market portfolio. The…

This work studies the deep learning-based numerical algorithms for optimal hedging problems in markets with general convex transaction costs on the trading rates, focusing on their scalability of trading time horizon. Based on the…

We study the upper and lower bounds for prices of European and American style options with the possibility of an external termination, meaning that the contract may be terminated at some random time. Under the assumption that the underlying…

This paper characterizes the probability of a market failure defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through…

We consider a global market constituted by several submarkets, each with its own assets and num\'eraire. We provide theoretical foundations for the existence of equivalent martingale measures and results on superreplication prices which…

We describe the bailout of banks by governments as a Markov Decision Process (MDP) where the actions are equity investments. The underlying dynamics is derived from the network of financial institutions linked by mutual exposures, and the…

In this paper, we present a novel computational framework for portfolio-wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. The new method…

Automated Market Makers (AMMs) are a class of smart contracts on Ethereum and other blockchains that "make markets" autonomously. In other words, AMMs stand ready to trade with other market participants that interact with them, at the…

We propose a new model for the joint evolution of the European inflation rate, the European Central Bank official interest rate and the short-term interest rate, in a stochastic, continuous time setting. We derive the valuation equation for…

Given the promising results on joint modeling of SPX/VIX smiles of the recently introduced quadratic rough Heston model, we consider a multi-asset market making problem on SPX and its derivatives, e.g. VIX futures, SPX and VIX options. The…

We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP)…

Technology trends as digitalization and Industry 4.0 initiate a growing demand for new business models. Most of this models requires a fundamental shift of operational and financial risks between seller and buyer. A key question is…

We propose a non-parametric extension with leverage functions to the Andersen commodity curve model. We calibrate this model to market data for WTI and NG including option skew at the standard maturities. While the model can be calibrated…

We study a continuous-time Markowitz mean-variance portfolio selection model in which a naive agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naive policies through the limit…

We extend upon the saddle-point equation presented in [1] to derive large-time model-implied volatility smiles, providing its theoretical foundation and studying its applications in classical models. As long as characteristic function…