Related papers: On a Nonlinear Partial Integro-Differential Equati…
We introduce a local volatility model for the valuation of options on commodity futures by using European vanilla option prices. The corresponding calibration problem is addressed within an online framework, allowing the use of multiple…
Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the…
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…
We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular we investigate the VXX notes tracking the short-end part of the futures term structure. Inspired by recent developments in…
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.…
We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
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…
We apply convex regularization techniques to the problem of calibrating the local volatility surface model of Dupire taking into account the practical requirement of discrete grids and noisy data. Such requirements are the consequence of…
The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the…
The Local Volatility model is a well-known extension of the Black-Scholes constant volatility model whereby the volatility is dependent on both time and the underlying asset. This model can be calibrated to provide a perfect fit to a wide…
Volatility smile and skewness are two key properties of option prices that are represented by the implied volatility (IV) surface. However, IV surface calibration through nonlinear interpolation is a complex problem due to several factors,…
We derive generalizations of Dupire formula to the cases of general stochastic drift and/or stochastic local volatility. First, we handle a case in which the drift is given as difference of two stochastic short rates. Such a setting is…
Mathematical models for financial asset prices which include, for example, stochastic volatility or jumps are incomplete in that derivative securities are generally not replicable by trading in the underlying. In earlier work (2004) the…
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…
We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model. This is the class of financial models that combines the local and stochastic volatility features and has been subject of the attention by many researchers…
We introduce the Local Occupied Volatility (LOV) model that sits between Dupire's local volatility and fully path-dependent dynamics. By design, the LOV model ensures automatic calibration to European vanilla options, while offering the…
We use modifications of the Adams method and very fast and accurate sinh-acceleration method of the Fourier inversion (iFT) (S.Boyarchenko and Levendorski\u{i}, IJTAF 2019, v.22) to evaluate prices of vanilla options; for options of…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas, options on realized variance or VIX options. These…