Related papers: Historical Backtesting of Local Volatility Model u…

In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a…

The dynamic hedging theory only makes sense in the setup of one given model, whereas the practice of dynamic hedging is just the opposite, with models fleeing after the data through daily recalibration. This is quite of a quantitative…

We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the…

We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…

Volatility is a quantity of measurement for the price movements of stocks or options which indicates the uncertainty within financial markets. As an indicator of the level of risk or the degree of variation, volatility is important to…

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…

In this paper, a new numerical method based on adaptive gradient descent optimizers is provided for computing the implied volatility from the Black-Scholes (B-S) option pricing model. It is shown that the new method is more accurate than…

This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio…

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…

We propose a new financial model, the stochastic volatility model with sticky drawdown and drawup processes (SVSDU model), which enables us to capture the features of winning and losing streaks that are common across financial markets but…

This paper shows how reinforcement learning can be used to derive optimal hedging strategies for derivatives when there are transaction costs. The paper illustrates the approach by showing the difference between using delta hedging and…

Backtest is a way of financial risk evaluation which helps to analyze how our trading algorithm would work in markets with past time frame. The high volatility situation has always been a critical situation which creates challenges for…

Real-world applications of machine learning models are often subject to legal or policy-based regulations. Some of these regulations require ensuring the validity of the model, i.e., the approximation error being smaller than a threshold. A…

Stochastic volatility models, where the volatility is a stochastic process, can capture most of the essential stylized facts of implied volatility surfaces and give more realistic dynamics of the volatility smile/skew. However, they come…

In the regime switching extension of Black-Scholes-Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered…

Modelling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black--Merton--Scholes model where it…

Data-driven models, especially deep learning classifiers often demonstrate great success on clean datasets. Yet, they remain vulnerable to common data distortions such as adversarial and common corruption perturbations. These perturbations…

We amend and extend the Chiarella model of financial markets to deal with arbitrary long-term value drifts in a consistent way. This allows us to improve upon existing calibration schemes, opening the possibility of calibrating individual…

We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European…

Accurate electricity price forecasting (EPF) is increasingly difficult in markets characterised by extreme volatility, frequent price spikes, and rapid structural shifts. Deep learning (DL) has been increasingly adopted in EPF due to its…