Modelling Callable Annuity Bonds with Interest-Only Optionality

In this paper an investigation of the pricing of callable annuities with interest-only (I-O) optionality is conducted. First the I-O optionality feature of callable annuities is introduced. Next an algorithm for pricing callable annuities with I-O optionality using the finite difference methodology, is formulated. This is then used to investigate optimal strategies of I-O bonds and impacts on prices from the I-O optionality. It is found that the I-O feature necessitates a simultaneous valuation of all elements of the callable I-O bond. Following this, the Greeks of the I-O bond are investigated. It is found that they are affected by the I-O feature, but only to a limited extent. Finally, a model of heterogenous prepayment decisions is incorporated into the framework. The model is extended to model heterogeneity in the I-O exercise decisions. The incorporation of heterogeneity in borrower decisions is found to lead to reasonable causalities

Guaranteeing benefits in generational pension plans

In this paper we analyze the possibilities of intergenerational risk sharing in a generational DB pension fund. Each generation is subject to discretionary investment, indexation and contribution policies, thereby losing intergenerational diversification gains. Intergenerational risk sharing is repaired by introducing contingent claims on the generational surplus or deficit. We find that in some circumstances the values of these options can be substantial

Optimal Mortgage Prepayment Under the Cox-Ingersoll-Ross Model

We study a parabolic variational inequality and associated free boundary problem (FBP) with financial applications. We consider a mortgage contract having the early termination option via prepayment under the Cox-Ingersoll-Ross (CIR) model for the short rate. The problem is of significant interest from both mathematical and economic points of view. The main difficulty is that the Black-Scholes-type partial differential equation (PDE) associated with the problem is not uniformly parabolic and therefore standard approaches have to be modified to treat the degeneracy of the PDE. Our main results are the existence and uniqueness of a solution to the variational inequality and the associated FBP; the free boundary represents optimal prepayment rate for the mortgage contract at each time prior to expiry. We establish regularity of the free boundary; several other properties of the free boundary are studied as well as the infinite horizon problem. From the financial point of view, the infinite horizon problem is interpreted as the mortgage prepayment problem when there is a long time to expiration. In solving the infinite horizon problem we obtain a critical rate, such that for mortgage rates below this critical rate, prepayment is never an optimal decision for a long times to expiration. With the existence of a unique solution to the FBP established, we conclude by performing a calibration of the CIR model to constant maturity Treasury yields and investigate numerical aspects of the variational inequality

Policy shifts and Markov-switching in financial markets

Veränderungen der Rahmenbedingungen auf Finanzmärkten müssen von ökonomischen und ökonometrischen Modellen sinnvoll erfasst werden. Diese Dissertation beschäftigt sich mit der Zinsdynamik im Vorfeld einer Währungsunion. Auf diese Dynamik aufbauend werden Optionen auf Nullkuponanleihen bewertet. Wird die veränderte Dynamik nicht beachtet kann es zum Teil zu erheblichen Fehlbewertungen kommen wie in einer Monte-Carlo Studie gezeigt wird. Ferner wird ein Markov-Switching GARCH-Modell entwickelt, welches verschiedene GARCH Variationen in den einzelnen Regimen zulässt. So sind erstmals auch Wechsel der Spezifikation in den einzelnen Regimen, wie z.B. EGARCH-GARCH Modelle möglich. Diese neue Modellklasse wird genutzt, um die Auswirkungen des Verbots ungedeckter Leerverkäufe auf ausgewählte Aktien zu untersuchen

Equity Research valuation fraport AG airport services worldwide

On March 11, 2020, Covid-19 was officially announced as a global pandemic inflicting global challenges, economic, financial, and healthcare crises. In its wake, the travel industry was set to a complete halt resulting in international passenger freefalls of 95% in the subsequent month. Thus far, airport stocks are still trading below cruising altitude, marking one of the most damaged industries worldwide. Therefore, this thesis aims to analyze the intrinsic value of Fraport AG – Airport Services Worldwide, to exploit the effect of the pandemic and form an investment decision. The recovery profile is determined by unfolding vaccination rollouts, lifting travel restrictions, and increasing consumer spending power. Based on these assumptions, the intrinsic value per share, derived from the DCF analysis, should be €65.54 as of December 31, 2021. Based on the closing price of €59.18, the upside potential amounts to 10.7% and suggests a buy recommendation in the short run. However, the share price is expected to grow at 8.2% CAGR to €89.70 in 2025, proposing a hold recommendation in the long run. Scenario, sensitivity, and Monte Carlo analyses reveal more upside potential. Lastly, the results are compared to the target price of AlsterResearch AG.A 11 de Março de 2020, a Covid-19 foi oficialmente anunciada como uma pandemia o que veio impor desafios globais, crises económicas, financeiras e nos sistemas de saúde. Por conseguinte, a indústria de viagens sofreu uma total interrupção, pelo que no mês seguinte se observou uma queda de 95% do número de passageiros internacionais. Até ao momento, as ações dos aeroportos estão ainda a ser negociadas abaixo da altitude de cruzeiro, pelo que é uma das indústrias mais perturbadas com a pandemia à escala mundial. Dessa forma, esta tese visa analisar o valor intrínseco da Fraport AG - Airport Services Worldwide, considerando o impacto da pandemia e assim propor uma recomendação de investimento. O perfil de recuperação é determinado pela ampliação dos planos de vacinação, pelo levantamento de restrições de viagem, e pelo aumento do poder de compra dos consumidores. Considerando estes pressupostos, o valor intrínseco por ação, resultado de uma análise DCF, será de 65,54€ à data de 31 de dezembro de 2021. Com base no preço de fecho de 59,18€, a ascendente potencial remonta a 10,7% e a recomendação é a realização de uma compra para o curto prazo. Contudo, espera-se que o preço da ação cresça a 8,2% CAGR para 89,70€ em 2025, propondo-se uma recomendação de manutenção da posição no longo prazo. As análises de diferentes cenários, sensibilidade, e Monte Carlo revelam um potencial mais positivo. Por último, os resultados são comparados com o preço alvo da AlsterResearch AG

Mathematical control theory and Finance

Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to find solutions to ”real life” problems, as is the case in robotics, control of industrial processes or finance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the financial analyst to possess a high level of mathematical skills. Conversely, the complex challenges posed by the problems and models relevant to finance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical finance. Up to now, other branches of control theory have found comparatively less application in financial problems. To some extent, deterministic and stochastic control theories developed as different branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these fields has intensified. Some concepts from stochastic calculus (e.g., rough paths) have drawn the attention of the deterministic control theory community. Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic control. We strongly believe in the possibility of a fruitful collaboration between specialists of deterministic and stochastic control theory and specialists in finance, both from academic and business backgrounds. It is this kind of collaboration that the organizers of the Workshop on Mathematical Control Theory and Finance wished to foster. This volume collects a set of original papers based on plenary lectures and selected contributed talks presented at the Workshop. They cover a wide range of current research topics on the mathematics of control systems and applications to finance. They should appeal to all those who are interested in research at the junction of these three important fields as well as those who seek special topics within this scope.info:eu-repo/semantics/publishedVersio

Valuation for an American Continuous-Installment Put Option on Bond under Vasicek Interest Rate Model

The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim's equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optimal stopping and exercise boundaries by quadrature formulas. Numerical results and discussions are provided

An Analysis of Occupational Pension Provision: From Evaluation to Redesign

Around the turn of the 21st century, the “perfect storm” implied by low interest rates, poor stock market returns and an ageing society led collective pension plans into underfunded situations and caused considerable concerns over their financial sustainability. This thesis analyzes the prevailing collective pension plans in the Netherlands and makes suggestions on improving the occupational pension provision in changing demographic, financial and regulatory environments. Chapter 2 probes the pension investment performance at the overall plan level. We find that pension plans on average do not outperform their pre-selected benchmarks, reflecting that trustees fail to select superior asset management strategies. Comparatively, however, large plans outperform their smaller peers. Chapter 3 investigates the strategic asset allocation of pension plans under market consistent valuation. We find that a slight change in the model specification of asset return dynamics can have a significant impact on the optimal mix. In chapter 4, we propose a new generational plan design and find that it provides higher value and welfare to participants when compared with the current collective plan design. This is due to the fact that it allows for risk sharing via time diversification of long-term investments and prevents a-priori value transfers. To allow for intergenerational risk sharing, in Chapter 5 we introduce further design improvements by having generations trade contingent claims among them. Our estimates show that the guarantees are affordable and the surplus call option has substantial value. The option prices also give an indication of value tranfers in traditional collective pension designs

Accountants\u27 index. Twenty-first supplement, a bibliography of accounting literature, January 1972-December 1972 (Inclusive)

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