Volatility Modeling & Forecasting

In this paper we study the Fourier estimator of Malliavin and Mancino for the spot volatility. We establish the convergence of the trigonometric polynomial to the volatility’s path in a setting that includes the following aspects. First, the volatility is required to satisfy a mild integrability con

We argue that negative skew and positive mean of the distribution of stock returns are largely due to the broken symmetry of stochastic volatility governing gains and losses. Starting with stochastic differential equations for stock returns and for stochastic volatility we argue that the distributio

The Heston stochastic volatility model is arguably, the most popular stochastic volatility model used to price and risk manage exotic derivatives. In spite of this, it is not necessarily easy to calibrate to the market and obtain stable exotic option prices with this model. This paper focuses on the

Financial exclusion constrains entrepreneurship, increases income volatility, and widens wealth gaps. Underbanked consumers in Istanbul often have no bureau file because their earnings and payments flow through informal channels. To study how such borrowers can be evaluated we create a synthetic dat

Volatility clustering is one of the most robust stylized facts of financial markets, yet it is typically detected using moment-based diagnostics or parametric models such as GARCH. This paper shows that clustered volatility also leaves a clear imprint on the time-reversal symmetry of horizontal visi

Multi-strategy hedge funds face a fundamental organizational choice: should analysts generating trading strategies communicate, and if so, how? We investigate this using 5-agent LLM-based trading systems across 450 experiments spanning 21 months, comparing five organizational structures from isolate

This paper develops a novel framework for modeling the variance swap of multi-asset portfolios by employing the generalized variance approach, which utilizes the determinant of the covariance matrix of the underlying assets. By specifying the distribution of the log returns of the underlying assets

We introduce a new risk modeling framework where chaotic attractors shape the geometry of Bayesian inference. By combining heavy-tailed priors with Lorenz and Rossler dynamics, the models naturally generate volatility clustering, fat tails, and extreme events. We compare two complementary approaches

A multi-factor extension of the Hobson and Rogers (HR) model, incorporating a quadratic variance function (QHR model), is proposed and analysed. The QHR model allows for greater flexibility in defining the moving average filter while maintaining the Markovian property of the original HR model. The u

This paper explores a comprehensive class of time-changed stochastic processes constructed by subordinating Brownian motion with Levy processes, where the subordination is further governed by stochastic arrival mechanisms such as the Cox Ingersoll Ross (CIR) and Chan Karolyi Longstaff Sanders (CKLS)

A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously addressed using deep neural networks, can be efficiently solved u

This note gives a bound on the error of the leading term of the $t\to 0$ asymptotic expansion of the Hartman-Watson distribution $θ(r,t)$ in the regime $rt=ρ$ constant. The leading order term has the form $θ(ρ/t,t)=\frac{“1”}{“2πt”}e^{"-\frac{1"}{“t”} (F(ρ)-π^2/2)} G(ρ) (1 + \vartheta(t,ρ))$, where

Pricing composite and quanto contracts requires a joint model of both the underlying asset and the exchange rate. In this contribution, we explore the potential of local-correlation models to address the challenges of calibrating synthetic quanto forward contracts and composite options quoted in the

Deep learning methods have become a widespread toolbox for pricing and calibration of financial models. While they often provide new directions and research results, their `black box’ nature also results in a lack of interpretability. We provide a detailed interpretability analysis of these methods

This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium are constant, which is unrealistic in the real market. To ad

We propose an efficient, accurate and reliable simulation scheme for the stochastic-alpha-beta-rho (SABR) model. The two challenges of the SABR simulation lie in sampling (i) integrated variance conditional on terminal volatility and (ii) terminal forward price conditional on terminal volatility and

This study proposes a new exact simulation scheme of the Ornstein-Uhlenbeck driven stochastic volatility model. With the Karhunen-Loève expansions, the stochastic volatility path following the Ornstein-Uhlenbeck process is expressed as a sine series, and the time integrals of volatility and variance

We establish the weak convergence of the intensity of a nearly-unstable Hawkes process with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market model where orders to buy or sell an asset arrive according to a Hawkes process with power-law kernel. After suitable r

We derive quantitative error bounds for deep neural networks (DNNs) approximating option prices on a $d$-dimensional risky asset as functions of the underlying model parameters, payoff parameters and initial conditions. We cover a general class of stochastic volatility models of Markovian nature as

We propose a new measure of systemic risk to analyze the impact of the major financial market turmoils in the stock markets from 2000 to 2023 in the USA, Europe, Brazil, and Japan. Our Implied Volatility Realized Volatility Systemic Risk Indicator (IVRVSRI) shows that the reaction of stock markets v