A barrier option is a derivative instrument whose payoff is dependent on the path of the underlying security up to maturity. We design a pricing system using Finite Differences to investigate the properties of and price options with exotic barrier features. The system determines the payoff,...

This paper introduces a new semi-parametric methodology for the implied volatility surface, which incorporates machine learning algorithms. Given a starting model, a tree boosting algorithm sequentially minimizes the residuals of observed and estimated implied volatility. To overcome the poor...

The aim of this paper is to investigate the theoretical and empirical pricing of the Chicago Board of Trade (CBOT) Treasury-bond futures. The difficulty to price it arises from its multiple interdependent embedded delivery options, which can be exercised at various times and dates during the...

The computation of Greeks is a fundamental task for risk managing of financial instruments. The standard approach to their numerical evaluation is via finite differences. Most exotic derivatives are priced via Monte Carlo simulation: in these cases, it is hard to find a fast and accurate...

The no Butterfly arbitrage domain of Gatheral SVI 5-parameters formula for the volatility smile has been recently described. It requires in general a numerical minimization of 2 functions altogether with a few root finding procedures. We study here the case of some sub-SVIs (all with 3...

Stochastic volatility models have grown in popularity in the past decade or two. However, for many stochastic volatility models, the functional form of volatility along with the description of the diffusion process for volatility have been posed with analytic convenience in mind. Here, we...

The Local Stochastic Volatility model is the main model used to take into account the correct pricing and hedging with the volatility dynamic.We introduce a new methodology that combines Singular perturbation analysis and exotic greek computation. We obtain asymptotic formulae for the LSV impact...

The present article revisits the Diffusion Operator Integral (DOI) variance reduction technique originally proposed in [HP02] and extends its theoretical concept to the pricing of American-style options under (time-homogeneous) Lévy stochastic differential equations. The resulting Jump...

This paper introduces a unified machine learning framework for solving general asset pricing problems. Building on representations of asset prices in discrete-time and continuous-time models, we develop a solution strategy using neural networks and further machine learning techniques to...