A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options

We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementationComment: 25 page

A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options

We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementationbackward stochastic differential equations, parallel computing, Monte- Carlo methods, non linear PDE, American options, local volatility model.

Valuation of Multiple Exercise Options

Multiple exercise options may be considered as generalizations of American-style options as they provide the holder more than one exercise right. Examples of financial derivatives and real options with these properties have become more prevalent over the past decade and appear in sectors ranging from insurance to energy industries. Throughout the thesis particular attention is paid to swing options although we note that the methods described are equally applicable to other types of multiple exercise options. This thesis presents two novel methods for pricing multiple exercise option by simulation; the forest of stochastic trees and the forest of stochastic meshes. The proposed methods are of particular use in cases where there are potentially a large number (3 or more) of assets underlying the contract and/or if a number of risk factors are desirable for modelling the underlying price process. These valuation methods result in positively- and negatively-biased estimators for the true option value. We prove the sign of the estimator bias and show that these estimators are consistent for the true option value. A confidence interval for the true option value is easily constructed. Examples confirm that the implementation of these methods is correct and consistent with the theoretical properties of the estimators. This thesis also explores in detail a number of methods meant to enhance the effectiveness of the proposed simulation methods. These include using high performance computing techniques which include both parallel computing techniques on CPU-clusters and General purpose Graphics Processing Units (GPGPU) that take advantage of relatively inexpensive processors. Additionally we explore bias-corrected estimators for the option values which attempt to estimate the bias introduced at each time step by the estimator and then subtract this result. These improvements are desirable due to the computationally intensive nature of both methods

The Evaluation of Gas Sales Agreements

A gas sales agreement, also called a gas swing contract, is an agreement between a supplier and a purchaser for the delivery of variable daily quantities of gas, between specified minimum and maximum daily limits, over a certain number of years at a strike price. The main constraint of such an agreement is that there is a minimum volume of gas for which the buyer will be charged at the end of the year, regardless of the actual quantity of gas taken. For multiple year contracts, there are also features called the make-up and carry-forward banks which add another level of complexity to the analysis. We propose a framework for pricing such multiple year contracts where both the gas price and strike price are stochastic processes. With the help of a two-dimensional trinomial tree, we are able to price such swing contracts with both make-up and carry-forward banks, and find the optimal daily decisions and the optimal yearly usage of the make-up and carry-forward banks. We also provide a detailed analysis of the different features that these contracts possess. Furthermore, another feature, called the indexation principle, is popular in real markets, under which the strike price is called the index. In each month, the value of the index is determined by the weighted average price of some energy products in the previous month. We design a lattice-based algorithm to price such swing contracts and find optimal daily decisions by using graphics processing units. Since the least-squares Monte Carlo method is well-known to handle sophisticated models, such as multi-factor models, models with regime-switching, or models with jumps, we build this method for the pricing of gas sales agreements and analyze the performance of it, especially the impacts of explanatory variables. With the help of concrete numerical examples, various features of such contracts with indexation are demonstrated

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma

Keskusteluavustimen kehittäminen kuulovammaisia varten automaattista puheentunnistusta käyttäen

Understanding and participating in conversations has been reported as one of the biggest challenges hearing impaired people face in their daily lives. These communication problems have been shown to have wide-ranging negative consequences, affecting their quality of life and the opportunities available to them in education and employment. A conversational assistance application was investigated to alleviate these problems. The application uses automatic speech recognition technology to provide real-time speech-to-text transcriptions to the user, with the goal of helping deaf and hard of hearing persons in conversational situations. To validate the method and investigate its usefulness, a prototype application was developed for testing purposes using open-source software. A user test was designed and performed with test participants representing the target user group. The results indicate that the Conversation Assistant method is valid, meaning it can help the hearing impaired to follow and participate in conversational situations. Speech recognition accuracy, especially in noisy environments, was identified as the primary target for further development for increased usefulness of the application. Conversely, recognition speed was deemed to be sufficient and already surpass the transcription speed of human transcribers.Keskustelupuheen ymmärtäminen ja keskusteluihin osallistuminen on raportoitu yhdeksi suurimmista haasteista, joita kuulovammaiset kohtaavat jokapäiväisessä elämässään. Näillä viestintäongelmilla on osoitettu olevan laaja-alaisia negatiivisia vaikutuksia, jotka heijastuvat elämänlaatuun ja heikentävät kuulovammaisten yhdenvertaisia osallistumismahdollisuuksia opiskeluun ja työelämään. Työssä kehitettiin ja arvioitiin apusovellusta keskustelupuheen ymmärtämisen ja keskusteluihin osallistumisen helpottamiseksi. Sovellus käyttää automaattista puheentunnistusta reaaliaikaiseen puheen tekstittämiseen kuuroja ja huonokuuloisia varten. Menetelmän toimivuuden vahvistamiseksi ja sen hyödyllisyyden tutkimiseksi siitä kehitettiin prototyyppisovellus käyttäjätestausta varten avointa lähdekoodia hyödyntäen. Testaamista varten suunniteltiin ja toteutettiin käyttäjäkoe sovelluksen kohderyhmää edustavilla koekäyttäjillä. Saadut tulokset viittaavat siihen, että työssä esitetty Keskusteluavustin on toimiva ja hyödyllinen apuväline huonokuuloisille ja kuuroille. Puheentunnistustarkkuus erityisesti meluisissa olosuhteissa osoittautui ensisijaiseksi kehityskohteeksi apusovelluksen hyödyllisyyden lisäämiseksi. Puheentunnistuksen nopeus arvioitiin puolestaan jo riittävän nopeaksi, ylittäen selkeästi kirjoitustulkkien kirjoitusnopeuden

FSCL: Homogeneous programming, scheduling and execution on heterogeneous platforms

The last few years has seen activity towards programming models, languages and frameworks to address the increasingly wide range and broad availability of heterogeneous computing resources through raised programming abstraction and portability across different platforms. The effort spent in simplifying parallel programming across heterogeneous platforms is often outweighed by the need for low-level control over computation setup and execution and by performance opportunities that are missed due to the overhead introduced by the additional abstraction. Moreover, despite the ability to port parallel code across devices, each device is generally characterised by a restricted set of computations that it can execute outperforming the other devices in the system. The problem is therefore to schedule computations on increasingly popular multi-device heterogeneous platforms, helping to choose the best device among the available ones each time a computation has to execute. Our Ph.D. research investigates the possibilities to address the problem of programming and execution abstraction on heterogeneous platforms while helping to dynamically and transparently exploit the computing power of such platforms in a device-aware fashion