相关论文: Regular Variation and Smile Asymptotics
A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking at short maturities. For that reason, we introduce the Stationary Heston model where we replace the…
In this paper, we consider a mean-reverting stochastic volatility equation with regime switching, and present some sufficient conditions for the existence of global positive solution, asymptotic boundedness in pth moment, positive…
The asymptotic behaviour, with respect to the large order, of the radii of starlikeness of two types of normalised Bessel functions is considered. We derive complete asymptotic expansions for the radii of starlikeness and provide recurrence…
We prove a Tauberian theorem for the Laplace--Stieltjes transform and Karamata-type theorems in the framework of regularly log-periodic functions. As an application we determine the exact tail behavior of fixed points of certain type…
We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its…
In this paper, we present a realized range-based multipower variation theory, which can be used to estimate return variation and draw jump-robust inference about the diffusive volatility component, when a high-frequency record of asset…
We present a stochastic-local volatility model for derivative contracts on commodity futures able to describe forward-curve and smile dynamics with a fast calibration to liquid market quotes. A parsimonious parametrization is introduced to…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
This paper investigates the second order asymptotic expansion for tail probabilities of discounted aggregate claims in continuous-time renewal risk models with constant interest force. Concretely, two types of continuous-time renewal risk…
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is…
In this work, we propose a class of importance sampling (IS) estimators for estimating the right tail probability of a sum of continuous random variables based on a change of variables to $L^1$ polar coordinates in which the radial and…
We consider random vectors $X$ that satisfy the equation in law $X=AX+B$, where $A$ is a given random diagonal matrix and $B$ a given random vector, both independent of $X$. It is well known by the works of Kesten and Goldie that the…
An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal…
In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the…
Under scenario of high frequency data, consistent estimator of realized Laplace transform of volatility is proposed by \citet{TT2012a} and related central limit theorem has been well established. In this paper, we investigate the asymptotic…
This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…
Let $\{X_t, t \geq 1\}$ be a sequence of identically distributed and pairwise asymptotically independent random variables with regularly varying tails and $\{ \Theta_t, t\geq1 \}$ be a sequence of positive random variables independent of…
We provide general conditions ensuring that the value functions of some nonlinear stopping problems with finite horizon converge to the value functions of the corresponding problems with infinite horizon. Our result can be formulated as…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is…