arXiv research

Investigates existence of affine models for Lévy-driven term structures.

We derive representations of local risk-minimization of call and put options for Barndorff-Nielsen and Shephard models: jump type stochastic volatility models whose squared volatility process is given by a non-Gaussian rnstein-Uhlenbeck process. The general form of Barndorff-Nielsen and Shephard models includes two par…

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

We examine the small expiry behaviour of European call options in stock price models of exponential Lévy type. In most cases of interest, we are able to identify the exact small expiry asymptotics. In "complete generality" we are able to show that the time value of the call option has O(τ) decay as τ(time to expiry) go…

The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.

A new method calculates implied volatilities without using option prices.

A new modelling approach that directly prescribes dynamics to the term structure of VIX futures is proposed in this paper. The approach is motivated by the tractability enjoyed by models that directly prescribe dynamics to the VIX, practices observed in interest-rate modelling, and the desire to develop a platform to b…

New formula for implied volatility from Black-Scholes model.

The asymptotic behavior of the implied volatility associated with a general call pricing function has been extensively studied in the last decade. The main topics discussed in this paper are Lee's moment formulas for the implied volatility, and Piterbarg's conjecture, describing how the implied volatility behaves in th…

This paper proposes a new framework for financial risk that considers predictability rather than volatility.

In this paper, we relax the power parameter of instantaneous variance and develop a new stochastic volatility plus jumps model that generalize the Heston model and 3/2 model as special cases. This model has two distinctive features. First, we do not restrict the new parameter, letting the data speak as to its direction…

In this paper, we give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter process $Θ= T^{-1} \int_0^T θ_t^* dt$. We provide a local parametric estimator (LPE) of $Θ$ and conditions u…

We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results like unconditional stability in the sense of von Neumann are presented. Where the a…

New stock market index captures market chaos and volatility.

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…

We introduce a multivariate stochastic volatility model for asset returns that imposes no restrictions to the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. When the number of assets is prohibitively large, we propose a factor multivariate stochastic volatili…

CRBMs improve financial regime detection with PCD and free energy analysis.

The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative and caplet and swaption prices can be calculated analytically. In order to guarantee nonnegative interest rates affine LIBOR models are driven by no…

Price and return predictions are limited by economic complexity, not just volatility.

We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices. Good-deal bounds are determined by a subset of risk-neutral pricing measures such that not only opportunities for arbitrage are excluded but also deals that are too good, by restricti…

We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most general context -- the impact of stochastic variables on the P&L of a hedged port…

Second-order economic theory considers new variables to improve price volatility predictions.

We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labordère [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance…

Proposes a Structural Matrix Autoregressive model for joint analysis of asset returns, realized volatility, and trading volume.

Deep neural networks can accurately approximate option prices in stochastic volatility models.

New machine learning model identifies key drivers of market troughs.

The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic volatility. Using the martingale approach, we prove the existence of the optimal stra…

New high-order approximations for CIR process using random grids.

The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary ergodic random process rapidly varying in time. We exploit the fact that…

We use commutator techniques and calculations in solvable Lie groups to investigate certain evolution Partial Differential Equations (PDEs for short) that arise in the study of stochastic volatility models for pricing contingent claims on risky assets. In particular, by restricting to domains of bounded volatility, we …

Develops high-order approximations for financial models, proving convergence and regularity.

Generative model prices basket options efficiently.

We propose a Bayesian non-parametric approach for modeling the distribution of multiple returns. In particular, we use an asymmetric dynamic conditional correlation (ADCC) model to estimate the time-varying correlations of financial returns where the individual volatilities are driven by GJR-GARCH models. The ADCC-GJR-…

We consider weighted directed networks for analysing, over the period 2000-2013, the interdependencies between volatilities of a large panel of stocks belonging to the S\&P100 index. In particular, we focus on the so-called {\it Long-Run Variance Decomposition Network} (LVDN), where the nodes are stocks, and the weight…

New method generates synthetic time series paths with more flexibility.

Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with respect to the time discretisation parameter and one half with respect to the space…

New method calibrates MQHawkes model using non-parametric approach, identifying cross-Hawkes and cross-leverage effects.

In the theory of riskfree hedges in continuous time finance, one can start with the delta-hedge and derive the option pricing equation, or one can start with the replicating, self-financing hedging strategy and derive both the delta-hedge and the option pricing partial differential equation. Approximately reversible tr…

Several studies explore inferences based on stochastic volatility (SV) models, taking into account the stylized facts of return data. The common problem is that the latent parameters of many volatility models are high-dimensional and analytically intractable, which means inferences require approximations using, for exa…

Study shows how China's stock market reflects economic demand changes during COVID-19.

New method recovers causal order from dependent data.

Deriving option prices from operational-time Markov lattices

We investigate the relative information content of six measures of dependence between two random variables $X$ and $Y$ for large or extreme events for several models of interest for financial time series. The six measures of dependence are respectively the linear correlation $ρ^+_v$ and Spearman's rho $ρ_s(v)$ conditio…

This study presents an agent-based computational cross-market model for Chinese equity market structure, which includes both stocks and CSI 300 index futures. In this model, we design several stocks and one index futures to simulate this structure. This model allows heterogeneous investors to make investment decisions …

We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model where the drift and volatility coefficients are general functions of the level of surplus and the external environment regime. The environment regime is modeled by a Markov process. Both cap…

Exact relationships found between ATM slope, volatility swap, and zero vanna.

Study local volatility from rough volatility models, finding new skew rule.

Paper derives formulas for volatility swap strike and zero vanna implied volatility.