A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study large deviations in fractional volatility models with non-Gaussian volatility.
We consider a stochastic volatility model where the moment generating function of the logarithmic price is finite only on part of the real line. Using a new Tauberian result obtained in [1] and [2], we show that the knowledge of the moment generating function near its critical moment gives a sharp asymptotic expansion …
The paper is concerned with the problem of existence of solutions for the Heath-Jarrow-Morton equation with linear volatility. Necessary conditions and sufficient conditions for the existence of weak solutions and strong solutions are provided. It is shown that the key role is played by the logarithmic growth condition…
The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the exist…
We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular, both mean and volatility are unbounded. We assume that there is Knightian uncertain…
In this note, we derive the characteristic function expansion for logarithm of the underlying asset price in corrected Heston model as proposed by Fouque and Lorig.
Study proves existence, uniqueness, and positivity of solutions to a complex volatility model.
Two new rational formulae for normal implied volatility are presented.
New rough stochastic volatility models using log-modulated fractional Brownian motion.
The study approximates option prices using Hermite polynomials without assuming a specific distribution.
Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and volume interact, particularly when the levels of both are high. We find that the…
This paper develops copula-based models for forecasting multivariate realized volatility.
Investor optimizes worst-case portfolio in uncertain markets.
We give explicit solutions for utility maximization of terminal wealth problem in the presence of Knightian uncertainty in continuous time in a complete market. We assume there is uncertainty on both drift and volatility of the underlying stocks, which induce nonequivalent measures on canonical space o…
A new model captures forward curve dynamics with stochastic volatility.
Study identifies key ESG variables for assessing financial risk.
This letter revisits the informational efficiency of the Bitcoin market. In particular we analyze the time-varying behavior of long memory of returns on Bitcoin and volatility 2011 until 2017, using the Hurst exponent. Our results are twofold. First, R/S method is prone to detect long memory, whereas DFA method can dis…
We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for…
The problem of existence of solution for the Heath-Jarrow-Morton equation with linear volatility and purely jump random factor is studied. Sufficient conditions for existence and non-existence of the solution in the class of bounded fields are formulated. It is shown that if the first derivative of the Levy-Khinchin ex…
Finance is about how the continuous stream of news gets incorporated into prices. But not all news have the same impact. Can one distinguish the effects of the Sept. 11, 2001 attack or of the coup against Gorbachev on Aug., 19, 1991 from financial crashes such as Oct. 1987 as well as smaller volatility bursts? Using a …
Hybrid GARCH-GRU model improves volatility forecasting for financial assets.
Modeling financial market dynamics with noise and fundamentalist agents.
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is non-dominated. We propose studying this p…
Revisits consumption-investment problem with anticipative noise.
The paper derives formulas for pricing geometric Asian options in the Volterra-Heston model.
We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible Lévy triplets; that is, possible instantaneous drift, volatility and jump characteristics of the price process. We show that an optimal investment…
We study convexity and monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide conditions under which convexity of the price in the short rate is guaranteed. Under these conditions the price is decreasing in the drift and increasing in the volatilit…
The relationship between price volatilty and a market extremum is examined using a fundamental economics model of supply and demand. By examining randomness through a microeconomic setting, we obtain the implications of randomness in the supply and demand, rather than assuming that price has randomness on an empirical …
Model monthly VIX and stock returns using log-Heston model.
In Europe, Germany is taking the lead in the switch from the conventional to renewable energy. This poses new challenges as wind and solar energy are fundamentally intermittent, weather-dependent and less predictable. It is therefore of considerable interest to investigate the evolution of price volatility in this post…
Study simulates Heston-type local stochastic volatility model using particle method.
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such a model is less studied in the literature. We show i…
We consider a general one-factor short rate model, in which the instantaneous interest rate is driven by a univariate diffusion with time independent drift and volatility. We construct recursive formula for the coefficients of the Taylor expansion of the bond price and its logarithm around , where is time to m…
We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that is, a simple arbitrage which promises a minimal riskless gain of ε, if the inves…
New method generates synthetic time series paths with more flexibility.
Modeling volatility with Chained Gamma Distributions for financial time series.
Modelling accurately financial price variations is an essential step underlying portfolio allocation optimization, derivative pricing and hedging, fund management and trading. The observed complex price fluctuations guide and constraint our theoretical understanding of agent interactions and of the organization of the …
Researchers tackle insider trading in incomplete markets using a discrete-time jump process approach.
Using ultra-high-frequency data extracted from the order flows of 23 stocks traded on the Shenzhen Stock Exchange, we study the empirical regularities of order placement in the opening call auction, cool period and continuous auction. The distributions of relative logarithmic prices against reference prices in the thre…
The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over , and it is the result of the non-Pearson type auto-correlations in the index. These non-Pearson type correlations can be viewed also as functionally dependent daily volatilities, ext…
Paper develops duality theory for robust utility maximization in continuous time.
In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notio…
Optimal dynamic fees for AMMs: A stochastic control approach
Study rigidity by logarithmic capacity and related functions.
Study real logarithms of semi-simple matrices, focusing on differential structure.
Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.
Logarithmic connections on principal bundles over normal varieties are studied.
We present a new method to solve certain -equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a -lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness…