Related papers: Filling the gaps smoothly
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 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 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…
We develop a non-parametric, semimartingale optimal transport, calibration methodology for local volatility models with stochastic interest rate. The method finds a fully calibrated model which is the closest, in a way that can be defined…
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…
Long maturity options or a wide class of hybrid products are evaluated using a local volatility type modelling for the asset price S(t) with a stochastic interest rate r(t). The calibration of the local volatility function is usually…
We study the problem of reconstruction of special special time dependent local volatility from market prices of options with different strikes at two expiration times. For a general diffusion process we apply the linearization technique and…
Consistently fitting vanilla option surfaces is an important issue when it comes to modelling in finance. Local volatility models introduced by Dupire in 1994 are widely used to price and manage the risks of structured products. However,…
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…
Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observable market data.…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
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…
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…
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.…
Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it…
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…
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…
This paper offers a new approach to modeling and forecasting of nonstationary time series with applications to volatility modeling for financial data. The approach is based on the assumption of local homogeneity: for every time point, there…
We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion…
This paper studies equity basket options -- i.e., multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks -- and develops a new and innovative approach to ensure consistency between options…