Related papers: Asymptotic analysis for stochastic volatility: Edg…

We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first…

In this paper, we consider the one-term Edgeworth expansion for finite population L-statistics. We provide an explicit formula for the Edgeworth correction term and give sufficient conditions for the validity of the expansion which are…

In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion…

In this paper, we consider the sphericity test for a one-sample problem under high-dimensional two-step monotone incomplete data. Existing asymptotic expansions for the null distributions of the likelihood ratio test (LRT) statistic and…

In this article, we derive the asymptotic expansion, up to an arbitrary order in theory, for the solution of a two-dimensional elliptic equation with strongly anisotropic diffusion coefficients along different directions, subject to the…

We analyze the empirical performance of several non-parametric estimators of the pricing functional for European options, using historical put and call prices on the S&P500 during the year 2012. Two main families of estimators are…

In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as…

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…

Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…

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…

European options can be priced when returns follow a Student's t-distribution, provided that the asset is capped in value or the distribution is truncated. We call pricing of options using a log Student's t-distribution a Gosset approach,…

We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…

Using the option delta systematically, we derive tighter lower and upper bounds of the Black-Scholes implied volatility than those in Tehranchi [SIAM J. Financ. Math. 7 (2016), 893-916]. As an application, we propose a Newton-Raphson…

Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…

We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…

This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research…

We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of…

We study the numerical evaluation of several functions appearing in the small time expansion of the distribution of the time-integral of the geometric Brownian motion as well as its joint distribution with the terminal value of the…

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.

This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation…