arXiv subjects

Ludovic Goudenege

Publications and source records attributed to Ludovic Goudenege.

4 recordsLinked to original sources

arXiv2026

Market-Informed Valuation of GMMB Riders with Surrender Options under a Heston Stochastic-Local Volatility Model

We develop a market-informed valuation framework for guaranteed minimum maturity benefit (GMMB) riders with rational surrender under the Heston stochastic-local volatility (SLV) model. The guarantee is written on the fee-deducted account value and is considered both in its terminal-only form and in the presence of early surrender rights. The Heston SLV specification combines stochastic volatility with a leverage function calibrated to a prescribed local-volatility surface. The leverage surface is obtained through a forward Markovian-projection equation so that, at the model level, the SLV dynamics are constrained to the same one-dimensional marginals as the corresponding local-volatility (LV) model. The latter is used only as a one-factor benchmark, allowing us to isolate the effect of stochastic volatility on continuation values and surrender decisions while preserving the same option-calibrated local-volatility target. We derive the associated backward pricing equations and propose a hybrid tree/finite-difference algorithm for the SLV model with a calibrated leverage function. Synthetic experiments and a market-informed case study show that SLV and LV valuations are numerically close for terminal-only guarantees, as expected from the common marginal target, whereas materially larger differences can arise once surrender is allowed. These differences are reflected in guarantee values, fair insurance fees and volatility-dependent surrender regions. The results indicate that matching one-date marginals implied by vanilla-option prices does not eliminate model risk for insurance liabilities whose value depends on conditional continuation dynamics and endogenous surrender decisions.

q-fin.CP↗

arXiv2025

Leveraging Machine Learning for High-Dimensional Option Pricing within the Uncertain Volatility Model

This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent unpredictability of market volatility by setting upper and lower bounds on volatility and the correlation among underlying assets. By integrating advanced Machine Learning algorithms, we aim to enhance the accuracy and efficiency of option pricing under the UVM, especially when the option price depends on a large number of variables, such as in basket or path-dependent options. In this paper, we consider two approaches based on Machine Learning. The first one, termed GTU, evolves backward in time, dynamically selecting at each time step the most expensive volatility and correlation for each market state. Specifically, it identifies the particular values of volatility and correlation that maximize the expected option value at the next time step, and therefore, an optimization problem must be solved. This is achieved through the use of Gaussian Process regression, the computation of expectations via a single step of a multidimensional tree and the Sequential Quadratic Programming optimization algorithm. The second approach, referred to as NNU, leverages neural networks and frames pricing in the UVM as a control problem. Specifically, we train a neural network to determine the most adverse volatility and correlation for each simulated market state, generated via random simulations. The option price is then obtained through Monte Carlo simulations, which are performed using the values for the uncertain parameters provided by the neural network. The numerical results demonstrate that the proposed approaches can significantly improve the precision of option pricing particularly in high-dimensional contexts.

q-fin.CP↗

arXiv2022

Computing XVA for American basket derivatives by Machine Learning techniques

Total value adjustment (XVA) is the change in value to be added to the price of a derivative to account for the bilateral default risk and the funding costs. In this paper, we compute such a premium for American basket derivatives whose payoff depends on multiple underlyings. In particular, in our model, those underlying are supposed to follow the multidimensional Black-Scholes stochastic model. In order to determine the XVA, we follow the approach introduced by Burgard and Kjaer \cite{burgard2010pde} and afterward applied by Arregui et al. \cite{arregui2017pde,arregui2019monte} for the one-dimensional American derivatives. The evaluation of the XVA for basket derivatives is particularly challenging as the presence of several underlings leads to a high-dimensional control problem. We tackle such an obstacle by resorting to Gaussian Process Regression, a machine learning technique that allows one to address the curse of dimensionality effectively. Moreover, the use of numerical techniques, such as control variates, turns out to be a powerful tool to improve the accuracy of the proposed methods. The paper includes the results of several numerical experiments that confirm the goodness of the proposed methodologies.

q-fin.CP↗

arXiv2015

Pricing and Hedging GLWB in the Heston and in the Black-Scholes with Stochastic Interest Rate Models

Valuing Guaranteed Lifelong Withdrawal Benefit (GLWB) has attracted significant attention from both the academic field and real world financial markets. As remarked by Forsyth and Vetzal the Black and Scholes framework seems to be inappropriate for such long maturity products. They propose to use a regime switching model. Alternatively, we propose here to use a stochastic volatility model (Heston model) and a Black Scholes model with stochastic interest rate (Hull White model). For this purpose we present four numerical methods for pricing GLWB variables annuities: a hybrid tree-finite difference method and a hybrid Monte Carlo method, an ADI finite difference scheme, and a standard Monte Carlo method. These methods are used to determine the no-arbitrage fee for the most popular versions of the GLWB contract, and to calculate the Greeks used in hedging. Both constant withdrawal and optimal withdrawal (including lapsation) strategies are considered. Numerical results are presented which demonstrate the sensitivity of the no-arbitrage fee to economic, contractual and longevity assumptions.

q-fin.PR↗