相关论文: Asymptotic equivalence in Lee's moment formulas fo…
The correlated stochastic volatility models constitute a natural extension of the Black and Scholes-Merton framework: here the volatility is not a constant, but a stochastic process correlated with the price log-return one. At present,…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment $s_+$ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility…
Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton…
We investigate the concept of an asymptotic e-process, which is a doubly-indexed stochastic process $(E_{m,n})_{m,n\in\mathbb{N}}$ that possesses, asymptotically for an approximation index $m\to\infty$, the properties of an e-process along…
We solve the pricing problem for perpetual American puts and calls on dividend-paying assets. The dependence of a dividend process on the underlying stochastic factor is fairly general: any non-decreasing function is admissible. The…
Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential L\'evy models based on prices of European options. To this end, we show joint asymptotic normality in the spectral calibration…
We introduce the notion of continuously invertible volatility models that relies on some Lyapunov condition and some regularity condition. We show that it is almost equivalent to the ability of the volatilities forecasting using the…
We study the asymptotic behaviour of additive functionals of random walks in random scenery. We establish bounds for the moments of the local time of the Kesten and Spitzer process.These bounds combined with a previous moment convergence…
A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…
We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is…
A third-order approximation for close-to-the-money European option prices under an infinite-variation CGMY L\'{e}vy model is derived, and is then extended to a model with an additional independent Brownian component. The asymptotic regime…
The formation of price in a financial market is modelled as a chain of Ising spin with three fundamental figures of trading. We investigate the time behaviour of the model, and we compare the results with the real EURO/USD change rate. By…
In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure $P$ and corresponding martingale measure $Q$ change to $\tilde{P}$ and $\tilde{Q}$ respectively. Then, we…
We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
Most of the existing methods for pricing Asian options are less efficient in the limit of small maturities and small volatilities. In this paper, we use the large deviations theory for the analysis of short-maturity Asian options. We…
Dynamic hedging of an European option under a general local volatility model with small linear transaction costs is studied. A continuous control version of Leland's strategy that asymptotically replicates the payoff is constructed. An…