Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging

We study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this vanilla option, delta-vega hedging is asymptotically optimal in the limit for small uncertainty aversion. The corresponding indifference price corrections are determined by the disparity between the vegas, gammas, vannas, and volgas of the non-traded and the liquidly traded options.Comment: 44 pages; forthcoming in 'Finance and Stochastics

Pricing Models for Bermudan-Style Interest Rate Derivatives

Bermuda-stijl rente derivaten vormen een belangrijke klasse van opties. Veel bancaire en verzekeringsproducten, zoals hypotheken, vervroegd aflosbare obligaties, en levensverzekeringen, bevatten Bermuda rente opties, die een gevolg zijn van de mogelijkheid tot vervroegde terugbetaling of stopzetting van het contract. Het veel voorkomen van deze opties maakt duidelijk dat het belangrijk is, voor banken en verzekeraars, om de waarde en risico van deze producten op de juiste manier in te schatten. Het juist inschatten van het risico maakt het mogelijk om markt risico af te dekken met onderliggende en regelmatig verhandelde waardes en opties. Waarderingsmodellen moeten arbitrage-vrij zijn, en dienen gekalibreerd te zijn aan prijzen van actief verhandelde onderliggende opties. De dynamica van de modellen moet overeen komen met de geobserveerde dynamica van de rente-termijnstructuur, zoals bijvoorbeeld correlatie tussen rentestanden. Bovendien moeten waarderingsalgoritmes efficiënt zijn: Financiële beslissingen gebaseerd op derivaten waarderingsberekeningen worden veeleer binnen enkele seconden genomen, dan binnen uren of dagen. In recente jaren is een succesvolle klasse van modellen naar voren gekomen, genaamd markt modellen. Dit proefschrift breidt de theorie van markt modellen uit, door: (i) een nieuwe, efficiënte en meer nauwkeurige benaderende waarderingstechniek te introduceren, (ii) twee nieuwe en snelle algoritmes voor correlatie-kalibratie te presenteren, (iii) nieuwe modellen te ontwikkelen die een efficiënte kalibratie toestaan voor een hele nieuwe klasse van derivaten, zoals vaste-looptijd Bermuda rente opties, en (iv) nieuwe empirische vergelijkingen te presenteren van bestaande kalibratie technieken en modellen, in termen van reductie van risico.Bermudan-style interest rate derivatives are an important class of options. Many banking and insurance products, such as mortgages, cancellable bonds, and life insurance products, contain Bermudan interest rate options associated with early redemption or cancellation of the contract. The abundance of these options makes evident that their proper valuation and risk measurement are important to banks and insurance companies. Risk measurement allows for offsetting market risk by hedging with underlying liquidly traded assets and options. Pricing models must be arbitrage-free, and calibrated to prices of actively traded underlying options. Model dynamics need be consistent with observed dynamics of the term structure of interest rates, e.g., correlation. Moreover, valuation algorithms need be efficient: Derivatives pricing calculations need be performed in seconds, rather than hours or days. Recently, a successful class of models appeared in the literature known as market models. This thesis extends market model theory: (i) it introduces a new, efficient, and more accurate approximate pricing technique, (ii) it presents two new fast algorithms for correlation-calibration, (iii) it develops new models enabling efficient calibration for a new range of derivatives, such as fixed-maturity Bermudan swaptions, and (iv) it presents novel empirical comparisons of hedge performance of existing calibrations and models.Raoul Pietersz was born on 12 June 1978 in Rotterdam, The Netherlands. In 2000, he obtained a Certificate of Advanced Studies in Mathematics (Mathematical Tripos Part III), with distinction, from the University of Cambridge. Over the academic year 1999-2000, he was awarded a title of Cambridge European Trust Scholar, and a retrospective title of Scholar at Peterhouse, Cambridge. In the summer of 2000, he completed internships at UBS Warburg and Dresdner Kleinwort Wasserstein, in London. In 2001, he obtained a first class M.Sc. degree in Mathematics from Leiden University. His Master’s thesis entitled “The LIBOR market model”was completed during an internship at ABN AMRO Bank, in Amsterdam. Over the period 1997-2001, he was awarded the Shell International Scholarship for undergraduate studies. His Ph.D. research, under supervision of Antoon Pelsser and Ton Vorst, focuses on the efficient valuation and risk management of interest rate derivatives. He has published articles in The Journal of Computational Finance, The Journal of Derivatives, Quantitative Finance, Risk Magazine and Wilmott Magazine. He has presented his research at various international conferences. His teaching experience includes lecturing taught Master courses on derivatives at the Rotterdam School of Management. Since the start of the Ph.D. period, he has held a part-time position at ABN AMRO Bank, initially at Quantitative Risk Analytics, Risk Management. Since July 2004, he is a Senior Derivatives Researcher, developing front-office pricing models for interest rate derivatives, at Product Development Group, Quantitative Analytics, as part of Structured Derivatives

Adapted Wasserstein Distances and Stability in Mathematical Finance

Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility that Q does not provide an "exact" description of reality. This leads us to the following question: will the hedge still be somewhat meaningful for models in the proximity of Q? If we measure proximity with the usual Wasserstein distance (say), the answer is NO. Models which are similar w.r.t. Wasserstein distance may provide dramatically different information on which to base a hedging strategy. Remarkably, this can be overcome by considering a suitable "adapted" version of the Wasserstein distance which takes the temporal structure of pricing models into account. This adapted Wasserstein distance is most closely related to the nested distance as pioneered by Pflug and Pichler \cite{Pf09,PfPi12,PfPi14}. It allows us to establish Lipschitz properties of hedging strategies for semimartingale models in discrete and continuous time. Notably, these abstract results are sharp already for Brownian motion and European call options.Comment: An author's name had been wrongfully give

Sensitivity of robust optimization problems under drift and volatility uncertainty

We examine optimization problems in which an investor has the opportunity to trade in $d$ stocks with the goal of maximizing her worst-case cost of cumulative gains and losses. Here, worst-case refers to taking into account all possible drift and volatility processes for the stocks that fall within a $\varepsilon$-neighborhood of predefined fixed baseline processes. Although solving the worst-case problem for a fixed $\varepsilon>0$ is known to be very challenging in general, we show that it can be approximated as $\varepsilon\to 0$ by the baseline problem (computed using the baseline processes) in the following sense: Firstly, the value of the worst-case problem is equal to the value of the baseline problem plus $\varepsilon$ times a correction term. This correction term can be computed explicitly and quantifies how sensitive a given optimization problem is to model uncertainty. Moreover, approximately optimal trading strategies for the worst-case problem can be obtained using optimal strategies from the corresponding baseline problem

Calibration of pricing models to bitcoin options

A type of derivatives, which use crpytocurrency as an underlying asset has become more popular during the past years as they offer alternative solutions to traditional financial instruments. Even though the dynamics and pricing principles of different financial derivatives have been rather popular subjects in quantitative finance, the literature on crypto derivatives has been rather scarce. The calibration of the pricing model is often considered an essential part of the derivative pricing, aiming to find the optimal parameters of a certain model through the pricing data available. This is typically done by using the quoted market prices or quoted implied volatilities. Even though the obtained parameters are primarily for pricing purposes, they also give valuable information about the characteristics of the underlying asset. The purpose of this thesis is to conduct a calibration of asset pricing models to the European-style call options, which use the bitcoin as an underlying asset. The option data involved was acquired from the Deribit cryptocurrency exchange from the review period of September 30th 2021 to October 31st 2021. With respect to the model calibrations, the stochastic volatility models of Heston and Bates are applied here. The calibrations of both models are carried out once per day across the review period by applying implied volatilities. With each calibration, a quoted implied volatility surface is established to which the model is calibrated. The study aims primarily at analysing the calibrated parameters and their development throughout the review period. On top of that, this study aims at answering what kind of implied volatility surfaces European-style bitcoin call options develop, and how these change across the review period. Based on the calibration results both models produce relatively good implied volatility surface fits, especially for short maturities. The obtained parameters support the volatile behaviour of bitcoin and the positive correlation between returns and volatility, which is not uncommon in the crypto markets. The results also show that certain parameters have a more significant impact on the final outcome. Despite a few exceptions, the parameters remain rather stable across the review period. Based on the established implied volatility surfaces, the variation throughout the review period is relatively large. However, when comparing the formed implied volatility surfaces to the ones found in previous studies and literature, many similarities can be found. During the review period, each IV surface provides a rather clear smile effect at short time to maturities, but there is a tendency of a forward skewed shape when maturities increase. This also highlights the growing demand of OTM- options in order to better hedge the price risk of bitcoin

Renewing Local Planning to Face Climate Change in the Tropics

This book aims to inspire decision makers and practitioners to change their approach to climate planning in the tropics through the application of modern technologies for characterizing local climate and tracking vulnerability and risk, and using decision-making tools. Drawing on 16 case studies conducted mainly in the Caribbean, Central America, Western and Eastern Africa, and South East Asia it is shown how successful integration of traditional and modern knowledge can enhance disaster risk reduction and adaptation to climate change in the tropics. The case studies encompass both rural and urban settings and cover different scales: rural communities, cities, and regions. In addition, the book looks to the future of planning by addressing topics of major importance, including residual risk integration in local development plans, damage insurance and the potential role of climate vulnerability reduction credits. In many regions of the tropics, climate planning is growing but has still very low quality. This book identifies the weaknesses and proposes effective solutions

Renewing Local Planning to Face Climate Change in the Tropics

climate vulnerability; urban resilience; climate change; adaptation; planning; environmental risk analysis; decision making; disaster risk reduction; tropical climate managemen

Renewing Local Planning to Face Climate Change in the Tropics

climate vulnerability; urban resilience; climate change; adaptation; planning; environmental risk analysis; decision making; disaster risk reduction; tropical climate managemen

Mid-century gothic : the agency and intimacy of uncanny objects in post-war British literature and culture

This thesis reassesses the years 1945-1955 as a hingepoint in British culture, a moment when literature, film and art responded to the wartime hiatus of consumer capitalism by resisting the turn towards conspicuous consumption and selfcommodification. This resistance can be discerned in a gothic impulse in post-war culture, in which uncanny encounters with haunted, recalcitrant or overassertive objects proliferated, and provided a critique of the subject/object relationship on which consumerism was predicated. In the opening chapter, the ubiquity of bombsite rubble is brought into dialogue with mid-century mural painting both in literature and at the Festival of Britain. In the second chapter, Barbara Jones’s Black Eyes and Lemonade exhibition of ephemera is considered alongside the work of the Independent Group. The third chapter examines how the period’s new media and computing hardware further complicated the status of the subject, through an analysis of the work of George Orwell, Alan Turing and William Grey Walter. In the fourth chapter, haunted furniture and domestic ephemera threaten to become rival subjectivities, in works including Elizabeth Bowen’s The Heat of the Day and Marghanita Laski’s The Victorian Chaise Longue. The fifth chapter considers the ways in which mid-century clothes and apparel enabled or restricted the autonomy of their wearers, through a comparative analysis of the Coronation, the British Everest expedition, and Britten’s coronation opera Gloriana. Finally, the onset of atomic anxiety is explored through stories about bombs, prosthetics and bodily penetration including Powell and Pressburger’s The Small Back Room. The thesis concludes that the intimacy and agency of these unruly objects remain as half-submerged cultural signposts offering an alternative understanding of twentieth-century materialism