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14 pages, 283 KiB

Open AccessArticle

Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options

by Guillaume Leduc

Mathematics 2025, 13(2), 213; https://doi.org/10.3390/math13020213 - 10 Jan 2025

Viewed by 564

American options have long received considerable attention in the literature, with numerous publications dedicated to their pricing. Bermudan and randomized Bermudan options are broadly used to estimate their prices efficiently. Notably, the penalty method yields option prices that coincide with those of randomized Bermudan options. However, theoretical results regarding the speed of convergence of these approximations to the American option price remain scarce. In this paper, we address this gap by establishing a general result on the convergence speed of Bermudan and randomized Bermudan option prices to their American limits. We prove that for convex payoff functions, the convergence speed is linear; that is, of order

1 / n

, where n denotes the number of exercisable opportunities in the Bermudan case and serves as the intensity parameter of the underlying Poisson process in the randomized Bermudan case. Our framework is quite general, encompassing Lévy models, stochastic volatility models, and nearly any risk-neutral model that can be incorporated within a strong Markov framework. We extend our analysis to Canadian options, showing under mild conditions a convergence rate of

1 / \sqrt{n}

to their American limits. To our knowledge, this is the first study addressing the speed of convergence in Canadian option pricing. Full article

(This article belongs to the Special Issue Financial Mathematics and Financial Engineering)

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15 pages, 299 KiB

Open AccessArticle

The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing

by Guillaume Leduc

Mathematics 2024, 12(7), 964; https://doi.org/10.3390/math12070964 - 24 Mar 2024

Cited by 1 | Viewed by 1779

Abstract

Oscillations in option price convergence have long been a problematic aspect of tree methods, inhibiting the use of repeated Richardson extrapolation that could otherwise greatly accelerate convergence, a feature integral to some of the most efficient modern methods. These oscillations are typically caused by the fluctuating positions of nodes around the discontinuities in the payoff function or its derivatives. Our paper addresses this crucial gap that typically prohibits the use of lattice methods when high efficiency is needed. Focusing on double barrier options, we develop a trinomial tree in which the positions of the nodes are precisely adjusted to align with these discontinuities throughout the option’s lifespan and across various time steps. This alignment enables the use of repeated extrapolation to achieve high order convergence, including near barriers, a well-known challenge in many tree methods. Maintaining the inherent simplicity and adaptability of tree methods, our approach is easily applicable to other models and option types. Full article

(This article belongs to the Special Issue Advances in Computational Methods for Finance and Insurance)

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33 pages, 570 KiB

Open AccessArticle

The Convergence Rate of Option Prices in Trinomial Trees

by Guillaume Leduc and Kenneth Palmer

Risks 2023, 11(3), 52; https://doi.org/10.3390/risks11030052 - 6 Mar 2023

Cited by 2 | Viewed by 4544

Abstract

We study the convergence of the binomial, trinomial, and more generally m-nomial tree schemes when evaluating certain European path-independent options in the Black–Scholes setting. To our knowledge, the results here are the first for trinomial trees. Our main result provides formulae for [...] Read more.

1 / \sqrt{n}

and

1 / n

in the expansion of the error for digital and standard put and call options. This result is obtained from an Edgeworth series in the form of Kolassa–McCullagh, which we derive from a recently established Edgeworth series in the form of Esseen/Bhattacharya and Rao for triangular arrays of random variables. We apply our result to the most popular trinomial trees and provide numerical illustrations. Full article

(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance II)

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23 pages, 14505 KiB

Open AccessArticle

Antimicrobial Resistance and Genetic Diversity of Pseudomonas aeruginosa Strains Isolated from Equine and Other Veterinary Samples

by Marine Pottier, Sophie Castagnet, François Gravey, Guillaume Leduc, Corinne Sévin, Sandrine Petry, Jean-Christophe Giard, Simon Le Hello and Albertine Léon

Pathogens 2023, 12(1), 64; https://doi.org/10.3390/pathogens12010064 - 30 Dec 2022

Cited by 15 | Viewed by 4147

Abstract

Pseudomonas aeruginosa is one of the leading causes of healthcare-associated infections in humans. This bacterium is less represented in veterinary medicine, despite causing difficult-to-treat infections due to its capacity to acquire antimicrobial resistance, produce biofilms, and persist in the environment, along with its limited number of veterinary antibiotic therapies. Here, we explored susceptibility profiles to antibiotics and to didecyldimethylammonium chloride (DDAC), a quaternary ammonium widely used as a disinfectant, in 168 P. aeruginosa strains isolated from animals, mainly Equidae. A genomic study was performed on 41 of these strains to determine their serotype, sequence type (ST), relatedness, and resistome. Overall, 7.7% of animal strains were resistant to carbapenems, 10.1% presented a multidrug-resistant (MDR) profile, and 11.3% showed decreased susceptibility (DS) to DDAC. Genomic analyses revealed that the study population was diverse, and 4.9% were ST235, which is considered the most relevant human high-risk clone worldwide. This study found P. aeruginosa populations with carbapenem resistance, multidrug resistance, and DS to DDAC in equine and canine isolates. These strains, which are not susceptible to antibiotics used in veterinary and human medicine, warrant close the setting up of a clone monitoring, based on that already in place in human medicine, in a one-health approach. Full article

(This article belongs to the Section Bacterial Pathogens)

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11 pages, 2012 KiB

Open AccessArticle

Role of Non-Invasive Respiratory Supports in COVID-19 Acute Respiratory Failure Patients with Do Not Intubate Orders

by Clément Medrinal, Alexis Gillet, Fairuz Boujibar, Jonathan Dugernier, Marcel Zwahlen, Bouchra Lamia, Christophe Girault, Jacques Creteur, Jean-Marc Fellrath, Laurence Haesler, Laurie Lagache, Laure Goubert, Elise Artaud Macari, Olivier Taton, Philippe Gouin, Dimitri Leduc, Olivier Van Hove, Michelle Norrenberg, Guillaume Prieur, Yann Combret, Nils Correvon, Roger Hilfiker and Olivier Contal Show full author list Hide full author list

J. Clin. Med. 2021, 10(13), 2783; https://doi.org/10.3390/jcm10132783 - 24 Jun 2021

Cited by 7 | Viewed by 4065

Abstract

The current gold-standard treatment for COVID-19-related hypoxemic respiratory failure is invasive mechanical ventilation. However, do not intubate orders (DNI), prevent the use of this treatment in some cases. The aim of this study was to evaluate if non-invasive ventilatory supports can provide a good therapeutic alternative to invasive ventilation in patients with severe COVID-19 infection and a DNI. Data were collected from four centres in three European countries. Patients with severe COVID-19 infection were included. We emulated a hypothetical target trial in which outcomes were compared in patients with a DNI order treated exclusively by non-invasive respiratory support with patients who could be intubated if necessary. We set up a propensity score and an inverse probability of treatment weighting to remove confounding by indication. Four-hundred patients were included: 270 were eligible for intubation and 130 had a DNI order. The adjusted risk ratio for death among patients eligible for intubation was 0.81 (95% CI 0.46 to 1.42). The median length of stay in acute care for survivors was similar between groups (18 (10–31) vs. (19 (13–23.5); p = 0.76). The use of non-invasive respiratory support is a good compromise for patients with severe COVID-19 and a do not intubate order. Full article

(This article belongs to the Section Respiratory Medicine)

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26 pages, 557 KiB

Open AccessArticle

Joshi’s Split Tree for Option Pricing

by Guillaume Leduc and Merima Nurkanovic Hot

Risks 2020, 8(3), 81; https://doi.org/10.3390/risks8030081 - 1 Aug 2020

Cited by 4 | Viewed by 3804

Abstract

In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a “flexible” version of Joshi’s tree, [...] Read more.

1 / n

and

1 / n^{3 / 2}

in the expansion of the error. Then we define several optimized versions of the tree, and find closed form formulae for the parameters of these optimal variants. In a numerical study, we found that in the American case, an optimized variant of the tree significantly improved the performance of Joshi’s original split tree. Full article

(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance)

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17 pages, 2177 KiB

Open AccessArticle

Heat Recovery for next Generation of Hybrid Vehicles: Simulation and Design of a Rankine Cycle System

by Alexandre Duparchy, Pierre Leduc, Guillaume Bourhis and Cyprien Ternel

World Electr. Veh. J. 2009, 3(3), 440-456; https://doi.org/10.3390/wevj3030440 - 25 Sep 2009

Cited by 9 | Viewed by 1169

Abstract

Improvement of vehicle effectiveness thanks to hybridisation are limited by the engine efficiency. In this way, the use of additional energy converters pave the way to a next generation of hybird vehicles.
After taking stock of the main sources of recoverable energy of a IC engine, this paper focuses on the Rankine cycle solution. This parametric study relies on a dedicated 0D/1D simulation tool to emphasize the effect of design and operating parameters on heat recovery potential and limitations. So, interactions between working fluid properties, pressure level in boiler and condenser, flow rate, component arrangement and engine operating conditions are discussed. Full article

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