arXiv research

We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge, corresponding to given log-price stochastic process, and in its close value, fo…

Study large deviations in fractional volatility models with non-Gaussian volatility.

This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: $dX_t=a_tdt+σ_tdW_t$, where $X$ denotes the log-price and $σ$ is a càdlàg semi-martingale. In the spirit of a series of recent works on the estimation of the cumulated volatility, we here focus …

This paper proposes new get-rich-quick schemes that involve trading in a financial security with a non-degenerate price path. For simplicity the interest rate is assumed zero. If the price path is assumed continuous, the trader can become infinitely rich immediately after it becomes non-constant (if it ever does). If i…

Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility follow a two-dimensional diffusion process where volatility is the stochastic d…

We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within $n$ subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high a…

The square root of Fredholm determinants causes numerical instabilities in option pricing models.

We study asymptotic properties of maximum likelihood estimators for Heston models based on continuous time observations of the log-price process. We distinguish three cases: subcritical (also called ergodic), critical and supercritical. In the subcritical case, asymptotic normality is proved for all the parameters, whi…

Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient point-wise homogeneous OHLC volatility estimators, valid for any price processes. We intr…

Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

The paper approximates CARMA models for option pricing.

In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the implied volatility. In addition, we prove that if the volatility function in an uncor…

This paper uses entropy to derive stock price dynamics and option valuation.

We propose a mathematical procedure for finding informed trader activities in European-style options and their underlying asset. The regression model (9) with moving average component was written. Being added to it ARMA-process for log-price differences of underlying asset, the generalized model is written as Vector AR…

In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model, which was recently introduced by Da Fonseca et al. \cite{DGT08}. Our method is based onanalysis of the conditional characteristic function of the log-price given volatility level. In particular, we…

We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an $α$-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the Lévy propagator. Using distributional and $\mathbb{C}^n$ tools, we derive an analytic …

In a series of recent papers Barndorff-Nielsen and Shephard introduce an attractive class of continuous time stochastic volatility models for financial assets where the volatility processes are functions of positive Ornstein-Uhlenbeck(OU) processes. This models are known to be substantially more flexible than Gaussian …

We consider the discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide and test an algorithm, which is based on the celebrated Foellmer-Schweizer decomp…

Study volatility models with rough paths, focusing on large deviations and option behavior.

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate this re…

Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an int…

We show how to price and replicate a variety of barrier-style claims written on the $\log$ price $X$ and quadratic variation $\langle X \rangle$ of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest rates. We model the risky asset as a strictly positive continuous semimartingale w…

Improved bounds for Black-Scholes volatility lead to faster root-finding.

Assuming that agents' preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer w…

We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling inert investors. With a suitable scaling, we show that when the price is driven …

FlashIV solves Black-Scholes implied volatility efficiently and accurately.

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Br…

Model predicts three market regimes: Good, Bad, and Ugly.

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strik…

In earlier studies, the estimation of the volatility of a stock using information on the daily opening, closing, high and low prices has been developed; the additional information in the high and low prices can be incorporated to produce unbiased (or near-unbiased) estimators with substantially lower variance than the …

This paper introduces an agent-based artificial financial market in which heterogeneous agents trade one single asset through a realistic trading mechanism for price formation. Agents are initially endowed with a finite amount of cash and a given finite portfolio of assets. There is no money-creation process; the total…

The Volterra Heston model is used to price American options.

We consider a class of asset pricing models, where the risk-neutral joint process of log-price and its stochastic variance is an affine process in the sense of Duffie, Filipovic and Schachermayer [2003]. First we obtain conditions for the price process to be conservative and a martingale. Then we present some results o…

We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the small-time limits of options…

The study explains why signature methods work in commodity futures term structure classification.

Proves existence and uniqueness of calibrated LSV model.

Realized statistics based on high frequency returns have become very popular in financial economics. In recent years, different non-parametric estimators of the variation of a log-price process have appeared. These were developed by many authors and were motivated by the existence of complete records of price data. Amo…

Classical time series models forecast Bitcoin prices and volatility accurately.

Study short-term behavior of up-and-in barrier options using Malliavin calculus.

The paper introduces a new volatility model using Fourier techniques for pricing and hedging.

We study fractional stochastic volatility models in which the volatility process is a positive continuous function $σ$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function $σ$ is globally…

The FSRM uses a multifractional process to capture price multifractality, revealing serial information for forecasting.

The paper explains how to predict returns based on firm characteristics.

Study the link between entropy and market efficiency using fractal properties.

We solve a family of fractional Riccati differential equations with constant (possibly complex) coefficients. These equations arise, e.g., in fractional Heston stochastic volatility models, that have received great attention in the recent financial literature thanks to their ability to reproduce a rough volatility beha…

Study on martingale property and moment explosions in signature volatility models.

Neural model improves option pricing by calibrating additive process term structure.