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We extend the application of the Cherny-Shiryaev-Yor invariance principle to a unified Bachelier-Black-Scholes-Merton (BBSM) dynamic pricing model. This extension incorporates the influence of the history of the dynamics (i.e., the path…
Starting from a basic model in which the dynamic of the transaction prices is a geometric Brownian motion disrupted by a microstructure white noise, corresponding to the random alternation of bids and asks, we propose moment-based…
We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a…
Sequential model-based optimization sequentially selects a candidate point by constructing a surrogate model with the history of evaluations, to solve a black-box optimization problem. Gaussian process (GP) regression is a popular choice as…
In the present paper we fill an essential gap in the Convertible Bonds pricing world by deriving a Binary Tree based model for valuation subject to credit risk. This model belongs to the framework known as Equity to Credit Risk. We show…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
Data mining methods have been widely applied in financial markets, with the purpose of providing suitable tools for prices forecasting and automatic trading. Particularly, learning methods aim to identify patterns in time series and, based…
We propose an innovative statistical method, called Ordinal Mixed-Effect Random Forest (OMERF), that extends the use of random forest to the analysis of hierarchical data and ordinal responses. The model preserves the flexibility and…
Random Forests (RF) are among the state-of-the-art in many machine learning applications. With the ongoing integration of ML models into everyday life, the deployment and continuous application of models becomes more and more an important…
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that…
Random Forests (RF) is a popular machine learning method for classification and regression problems. It involves a bagging application to decision tree models. One of the primary advantages of the Random Forests model is the reduction in…
In this paper, we address one of the main puzzles in finance observed in the stock market by proponents of behavioral finance: the stock predictability puzzle. We offer a statistical model within the context of rational finance which can be…
We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on $q$-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities…
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…
We compare the predictions of the stationary Kyle model, a microfounded multi-step linear price impact model in which market prices forecast fundamentals through information encoded in the order flow, with those of the propagator model, a…
In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed…
Cars are being sold more than ever. Developing countries adopt the lease culture instead of buying a new car due to affordability. Therefore, the rise of used cars sales is exponentially increasing. Car sellers sometimes take advantage of…
Random forests construct each tree with a different, randomised representation of the feature space. Their uniform voting cannot correct errors in regions where trees with incorrect representations probabilistically outnumber correct ones,…
While the market impact of aggressive orders has been extensively studied, the impact of passive orders, those executed through limit orders, remains less understood. The goal of this paper is to investigate passive market impact by…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…