Implied Volatilities of Caps: a Gaussian approach.

Implied volatilities of interest rate derivatives present some distinctive features, like the inverse relation with the underlying rates and the humped or decreasing shape of their term structure. The objective of this paper is to analyze and explain such features in a Gaussian framework. We will use an approximate relation which separates in a simple and natural way the effects on the implied volatility of the level and of the uncertainty of the interest rates. This is a useful tool for understanding the features of different models and to interpret some characteristics of the market.Implied volatility, forward rates, HJM models, calibration

Evaluating Discrete Dynamic Strategies in Affine Models

We consider the problem of measuring the performance of a dynamic strategy, rebalanced at a discrete set of dates, whose objective is that of replicating a claim in an incomplete market driven by a general multi-dimensional affine process. The main purpose of the paper is to propose a method to efficiently compute the expected value and variance of the hedging error of the strategy. Representing the pay-off the claim as an inverse Laplace transform, we are able to get semi-explicit formulas for strategies satisfying a certain property. The result is quite general and can be applied to a very rich class of models and strategies, including Delta hedging. We provide illustrations for the cases of interest rate models and Heston's stochastic volatility model.

Hedging error in Lévy models with a Fast Fourier Transform approach

We measure, in terms of expectation and variance, the cost of hedging a contingent claim when the hedging portfolio is re-balanced at a discrete set of dates. The basic point of the methodology is to have an integral representation of the payoff of the claim, in other words to be able to write the payoff as an inverse Laplace transform. The models under consideration belong to the class of Lévy models, like NIG, VG and Merton models. The methodology is implemented through the popular FFT algorithm, used by many financial institutions for pricing and calibration purposes. As applications, we analyze the effect of increasing the number of tradings and we make some robustness tests.Hedging, Lévy models, Fast Fourier Transform

Explicit formulas for the minimal variance hedging strategy in a martingale case

We explicitly compute the optimal strategy in discrete time for a European option and the variance of the corresponding hedging error under the hypothesis that the underlying is a martingale following a Geometric Brownian motion.minimal variance hedging

Measuring the error of dynamic hedging: a Laplace transform approach

We compute the expected value and the variance of the discretization error of delta hedging and of other strategies in the presence of proportional transaction costs. The method, based on Laplace transform, applies to a fairly general class of models, including Black-Scholes, Merton's jump-diffusion and Normal Inverse Gaussian. The results obtained are not asymptotical approximations but exact and efficient formulas, valid for any number of trading dates. They can also be employed under model mispecification, to measure the influence of model risk on a hedging strategy.hedging, Laplace transform

The Future of Sustainable Data Preparation

Data preparation has an important role in data analysis, and it is time and resource-consuming, both in terms of human and computational resources. The "Discount quality for responsible data science" project aims to focus on data-quality-based data preparation, analyzing the main characteristics of related tasks, and proposing methods for improving the sustainability of the data preparation tasks, considering also new emerging techniques based on generative AI. The paper discusses the main challenges that emerged in the initial research work in the project, as well as possible strategies for developing more sustainable data preparation frameworks

Explicit formulas for the minimal variance hedging strategy in a martingale case

Incomplete markets, Hedging, Contingent claim, Variance-optimal hedging,