Related papers: Historical Backtesting of Local Volatility Model u…
We study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this…
This paper studies empirical deep hedging for S&P 500 index options under a local downside-shortfall reward. It moves beyond performance comparison by asking what the learned hedge does, when it fails, and whether it can be made auditable.…
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 study the local volatility function in the Foreign Exchange market where both domestic and foreign interest rates are stochastic. This model is suitable to price long-dated FX derivatives. We derive the local volatility function and…
This paper proposes a deep delta hedging framework for options, utilizing neural networks to learn the residuals between the hedging function and the implied Black-Scholes delta. This approach leverages the smoother properties of these…
We develop deep learning models to learn the hedge ratio for S&P500 index options directly from options data. We compare different combinations of features and show that a feedforward neural network model with time to maturity,…
In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial…
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…
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…
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,…
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the…
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 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.…
This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a H\"older continuous payoff function in a local…
We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…
Local stochastic volatility refers to a popular model class in applied mathematical finance that allows for "calibration-on-the-fly", typically via a particle method, derived from a formal McKean-Vlasov equation. Well-posedness of this…
In this paper, we address the question of the optimal Delta and Vega hedging of a book of exotic options when there are execution costs associated with the trading of vanilla options. In a framework where exotic options are priced using a…
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…
We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…