This paper aims to examine how the radial basis function (RBF) technique works in the financial field, to compare the RBF performance with the results obtained with traditional methods (FDM, FEM), to choose the more suitable radial basis function to solve option pricing and to explain how its shape parameters can be set. It is crucial to set properly the shape parameter for the precision of the method and ultimately for the determination of the derivatives fair-value. Applying a maximum likelihood estimation (MLE), the authors propose a financial approach for its evaluation based on market/theoretical prices calibration.

Forecasting assets’ prices is the aim of each trader, although the trading approaches employed may vary a lot. The development of machine learning techniques has brought the opportunity to design mechanic trading systems based on dynamic artificial neural networks. The aim of this paper is to combine traditional technical indicators [such as exponential weighted moving average (EWMA), percentage volume oscillator (PVO) and stochastic indicator — %K and %D] with the nonlinear autoregressive networks (NAR and NARX). The first part of the paper describes how neural networks designed for forecasting time series work, the second one performs a deeper validation of the code and the third one combines the dynamic networks with traditional technical indicators in order to generate reliable mechanic signals. The article ends with a back testing of the trading system performed on Dow Jones Industrial Average and on Nasdaq Composite Indexes.

This article aims to estimate the fair-value of flexi-forwards, popular financial instruments on currencies, through Leisen–Reimer trees. The first part of paper deals with Markov chains suitable for pricing American options: Cox–Ross–Rubinstein, Jarrow–Rudd, Tian, Leisen–Reimer Trees. The correctness of the implementation in Matlab has been tested by comparing their prices with those obtained through approximated closed-formulas. The second part highlights the better performance of Leisen–Reimer trees in terms of convergence speed and sensitivity. Finally, flexi-forward contracts have been priced by using the numerical methodologies which have outperformed in the previous parts.

The estimation of partial derivatives of the price in respect to the main financial variables, called Greeks, is an essential task for a trader in order to understand the sensitivity of a derivative to the input of pricing model. The study of the level of reactivity of the mark to market is an essential task to manage properly the market risk of a portfolio. Due to the negative interest rates in Euro Area, the pricing model of interest-rates options (cap, floor and swaption) has been changed from a log-normal to a normal framework. The aim of this paper is to investigate the effects of this model change on the calculation of option sensitivities.

We provide the first formal investigation of the consequences of negative interest rates in the Eurozone on the pricing of interest rate options. Since the money market rates settled in negative territory and other market segments experienced negative yields, the broader financial community has had to face an unknown environment. The well-known Black–Scholes (BS) framework has become unfeasible for interest rate option valuation. First of all, no-arbitrage properties are breached, allowing arbitrage opportunities. More, the BS framework’s assumption of a log-normal distribution of the underlying rates does not stand with negative interest rates. We argue that the most notable approach which allows interest rate option pricing is [Bachelier, L (1900). Théorie de la speculation, 3rd Annales scientifiques de l’École Normale Supérieure 17, 21–86.], which assumes a normal distribution of the underlying rates. We demonstrate that the Bachelier model represents an answer to the critical issues that are raised in our study. Still, we highlight that it is far from being an accurate pricing model. Our research aims to light up an intense debate about alternative solutions among academics, financial professionals and institutions, and policy makers