Séminaire FDD-FiME

Elias Daboussi (Bank of America Merrill Lynch)   Titre: Modelling of CMS-Linked Products in an RFR framework Résumé:  Capitalizing on the Market’s adoption of Risk Free Rates (RFR) as benchmarks, we solve the problem of handling consistently single-expiry Interest Rates derivatives (e.g. CMS, CMS Spread-Options, Mid-Curves, Basket-Options etc..) in a way that respects the underlying swaps inter-dependencies as well as their volatilities across strikes and tenors, without resorting to arbitrary approximations routinely used in the industry. Introducing the convenient Annuity Due measure, we first show that the T-forward joint distribution of a family of RFR Swap Rates may be inferred explicitly from their options prices and correlation structure; we then design a numerical algorithm that allows the pricing of products sharing the same expiry using an efficient 1-step Monte Carlo scheme. Download slides

Workshop “Economic Modelling, Energy Markets and Decarbonation” October 12th, 2022 - Université Paris Dauphine - PSL // Room A707   2:30 pm Aude Pommeret (University of Savoie-Mont-Blanc) Title: Confronting the carbon pricing gap: Second best climate policy", co-écrit avec Francesco Ricci ( CEE-M, U. Montpellier), et Katheline Schubert (PSE, U. Paris 1). Abstract: Confronted with political opposition to the implementation of efficient direct carbon pricing, climate policy relies on alternative policy interventions, such as subsidies to renewables. This paper uses a dynamic macroeconomic model under a carbon budget to study climate policies constrained to keeping a constant level of the carbon tax. We find that it is possible to implement the optimal trajectory by combing an increasing tax on electricity consumption with a feed-in-premium paid to electricity produced from renewable sources. Otherwise, when the climate policy relies on the second instrument only, the subsidy to renewables should be so large to foster rapid build up of specialized capital, that it would imply large investment costs and financial burden on the public budget, unless the carbon tax level could be initially set at a high level. Unfortunately, the two solutions with no or low welfare losses raise concerns on their political acceptability too.  . . 3:15 pm Bert Willems (Tilburg University) Title: Bidding and Investment in Wholesale Electricity Markets: Pay-as-Bid versus Uniform-Price Auctions  Abstract: We compare two auction formats for wholesale electricity markets: uniform-price and pay-as-bid auctions, and study short-run bidding and long-run investment incentives. We develop a monopolistic competition model with a continuum of generation technologies from base-load to peak-load, and uncertain, elastic demand. Pay-as-bid auctions are shown to be inefficient because consumers' willingness to pay exceeds the marginal costs and producers' long-run investment incentives are distorted. The total installed capacity is the same, but the generation mix relies too little on baseload technologies. Consumer surplus is lower with pay-as-bid auctions, while under uniform-price auctions, consumer surplus is at the efficient level. . . 4:30 pm Stéphane Villeneuve (TSE) Title: Gaussian Agency problems with memory and Linear Contracts Abstract: Can a principal still offer optimal dynamic contracts that are linear in end-of-period outcomes even when the agent controls a process that exhibits memory? We provide a positive answer by extending the model of Holmstrom-Milgrom (1987) to general Gaussian settings where the output dynamics are not necessarily semi-martingales or Markov processes. We introduce a rich class of principal-agent models  that  encompasses dynamic agency models with memory. From the mathematical point of view, we develop a methodology to deal with the possible non-Markovianity and non-semimartingality of the control problem, which can no longer be directly solved by means of the usual Hamilton-Jacobi-Bellman equation. Our main contribution is to show that, for one-dimensional models, this setting always allows for optimal linear contracts in end-of-period observable outcomes with a  deterministic optimal level of effort.  In higher dimension, we show that linear contracts are still optimal when the effort cost function is radial and we quantify the gap between linear contracts and optimal contracts for more general quadratic costs of ...

Kang Liu (CMAP, Ecole Polytechnique) Title :  Large-scale nonconvex optimization: randomization, gap estimation, and numerical resolution Abstract : We address a large-scale and nonconvex optimization problem, involving an aggregative term. This term can be interpreted as the sum of the contributions of N agents to some common good, with N large. We investigate a relaxation of this problem, obtained by randomization. The relaxation gap is proved to converge to zeros as N goes to infinity, independently of the dimension of the aggregate. We propose a stochastic method to construct an approximate minimizer of the original problem, given an approximate solution of the randomized problem. McDiarmid's concentration inequality is used to quantify the probability of success of the method. We consider the Frank-Wolfe (FW) algorithm for the resolution of the randomized problem. Each iteration of the algorithm requires to solve a subproblem which can be decomposed into N independent optimization problems. A sublinear convergence rate is obtained for the FW algorithm. In order to handle the memory overflow problem possibly caused by the FW algorithm, we propose a stochastic Frank-Wolfe (SFW) algorithm, which ensures the convergence in both expectation and probability senses. Numerical experiments on a mixed-integer quadratic program and an aggregative optimal control problem illustrate the efficiency of the method. A joint work with J. Frédéric Bonnans, Nadia Oudjane, Laurent Pfeiffer, Cheng Wan Download slides