Related papers: Don't stay local - extrapolation analytics for Dup…
We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated…
In this paper we study the small noise asymptotic expansions for certain classes of local volatility models arising in finance. We provide explicit expressions for the involved coefficients as well as accurate estimates on the remainders.…
The paper proposes an expanded version of the Local Variance Gamma model of Carr and Nadtochiy by adding drift to the governing underlying process. Still in this new model it is possible to derive an ordinary differential equation for the…
The usage of a spot volatility estimate based on a volatility decomposition in a time-changed price-model according to the trading times is investigated. In this model clock-time volatility splits up into the product of tick-time volatility…
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…
In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed…
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility…
The calibration of a local volatility models to a given set of option prices is a classical problem of mathematical finance. It was considered in multiple papers where various solutions were proposed. In this paper an extension of the…
Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar…
In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to…
The feasibility of extrapolation of completely monotone functions can be quantified by examining the worst case scenario, whereby a pair of completely monotone functions agree on a given interval to a given relative precision, but differ as…
We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of It\^o semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of…
We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP)…
We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At…
We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset…
Local Volatility (LV) is a powerful tool for market modeling, enabling the generation of arbitrage-free scenarios calibrated to all European options. To implement LV, we need to interpolate and extrapolate option prices. This approach is…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
For quantitative trading risk management purposes, we present a novel idea: the realized local volatility surface. Concisely, it stands for the conditional expected volatility when sudden market behaviors of the underlying occur. One is…
This article addresses the problem of approximating the price of options on discrete and continuous arithmetic average of the underlying, i.e. discretely and continuously monitored Asian options, in local volatility models. A…
We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al.…