Integral Representation of Generalized Grey Brownian Motion

In this paper we investigate the representation of a class of non Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular the underlying process can be seen as a non Gaussian extension of the Ornstein-Uhlenbeck process, hence generalizing the representation results of Muravlev as well as Harms and Stefanovits to the non Gaussian case.Comment: arXiv admin note: text overlap with arXiv:1708.06784, arXiv:1807.0786

Modeling Large Spot Price Deviations in Electricity Markets

Increased insecurities on the energy markets have caused massive fluctuations of the electricity spot price within the past two years. In this work, we investigate the fit of a classical 3-factor model with a Gaussian base signal as well as one positive and one negative jump signal in this new market environment. We also study the influence of adding a second Gaussian base signal to the model. For the calibration of our model we use a Markov Chain Monte Carlo algorithm based on the so-called Gibbs sampling. The resulting 4-factor model is than compared to the 3-factor model in different time periods of particular interest and evaluated using posterior predictive checking. Additionally, we derive closed-form solutions for the price of futures contracts in our 4-factor spot price model. We find that the 4-factor model outperforms the 3-factor model in times of non-crises. In times of crises, the second Gaussian base signal does not lead to a better the fit of the model. To the best of our knowledge, this is the first study regarding stochastic electricity spot price models in this new market environment. Hence, it serves as a solid base for future research

Change of drift in one-dimensional diffusions

Funder: Johannes Kepler University LinzAbstractIt is generally understood that a given one-dimensional diffusion may be transformed by a Cameron–Martin–Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this, we have to know that the change-of-measure local martingale that we write down is a true martingale. We provide a complete characterisation of when this happens. This enables us to discuss the absence of arbitrage in a generalised Heston model including the case where the Feller condition for the volatility process is violated.</jats:p

Own-company stockholding and work effort preferences of an unconstrained executive

We develop a framework for analyzing an executive's own-company stockholding and work effort preferences. The executive, characterized by risk aversion and work effectiveness parameters, invests his personal wealth without constraint in the financial market, including the stock of his own company whose value he can directly influence with work effort. The executive's utility-maximizing personal investment and work effort strategy is derived in closed form, and a utility indifference rationale is applied to determine his required compensation. Being unconstrained byperformance contracting, the executive's work effort strategy establishes a base case for theoretical or empirical assessment of the benefits or otherwise of constraining executives with performance contracting

Nested MC-Based Risk Measurement of Complex Portfolios: Acceleration and Energy Efficiency

Risk analysis and management currently have a strong presence in financial institutions, where high performance and energy efficiency are key requirements for acceleration systems, especially when it comes to intraday analysis. In this regard, we approach the estimation of the widely-employed portfolio risk metrics value-at-risk (VaR) and conditional value-at-risk (cVaR) by means of nested Monte Carlo (MC) simulations. We do so by combining theory and software/hardware implementation. This allows us for the first time to investigate their performance on heterogeneous compute systems and across different compute platforms, namely central processing unit (CPU), many integrated core (MIC) architecture XeonPhi, graphics processing unit (GPU), and field-programmable gate array (FPGA). To this end, the OpenCL framework is employed to generate portable code, and the size of the simulations is scaled in order to evaluate variations in performance. Furthermore, we assess different parallelization schemes, and the targeted platforms are evaluated and compared in terms of runtime and energy efficiency. Our implementation also allowed us to derive a new algorithmic optimization regarding the generation of the required random number sequences. Moreover, we provide specific guidelines on how to properly handle these sequences in portable code, and on how to efficiently implement nested MC-based VaR and cVaR simulations on heterogeneous compute systems

Portfolio-Optimierung für leitende Angestellte

In this work, we develop a framework for analyzing an executive’s own- company stockholding and work effort preferences. The executive, character- ized by risk aversion and work effectiveness parameters, invests his personal wealth without constraint in the financial market, including the stock of his own company whose value he can directly influence with work effort. The executive’s utility-maximizing personal investment and work effort strategy is derived in closed form for logarithmic and power utility and for exponential utility for the case of zero interest rates. Additionally, a utility indifference rationale is applied to determine his fair compensation. Being unconstrained by performance contracting, the executive’s work effort strategy establishes a base case for theoretical or empirical assessment of the benefits or otherwise of constraining executives with performance contracting. Further, we consider a highly-qualified individual with respect to her choice between two distinct career paths. She can choose between a mid-level management position in a large company and an executive position within a smaller listed company with the possibility to directly affect the company’s share price. She invests in the financial market including the share of the smaller listed company. The utility maximizing strategy from consumption, investment, and work effort is derived in closed form for logarithmic utility and power utility. Conditions for the individual to pursue her career with the smaller listed company are obtained. The participation constraint is formulated in terms of the salary differential between the two positions. The smaller listed company can offer less salary. The salary shortfall is offset by the possibilityto benefit from her work effort by acquiring own-company shares. This givesinsight into aspects of optimal contract design. Our framework is applicable to the pharmaceutical and financial industry, as well as the IT sector.Wir entwickeln ein Modell zur Berechnung des in die eigenen Firmenaktien investierten Anteils und des Arbeitsaufwandes von leitenden Angestellten. Der leitende Angestellte - charakterisiert durch Risikoaversions- und Ar- beitseffektivitätsparameter - investiert sein Vermögen ohne Einschränkun- gen in den Finanzmarkt einschließlich der Aktie der eigenen Firma, deren Wert er durch seinen Arbeitsaufwand beeinflussen kann. Die nutzenmaxi- mierende Investitions- und Arbeitsaufwandsstrategie wird in geschlossener Form hergeleitet und mit einem Nutzenindifferenzargument die angemessene Entlohnung bestimmt. Der leitende Angestellte ist bei der Vertragserfüllung nicht eingeschränkt. Jedoch stellt die berechnete Arbeitsaufwandsstrategie einen Basisfall dar, der einen Einblick darin gibt, wie man die finanziellen Leistungen von leitenden Angestellten bemessen könnte und wie sie auf Ein- schränkungen bei der Vertragserfüllung reagieren könnten. Zudem betrach- ten wir ein hochqualifiziertes Individuum, das die Wahl zwischen zwei Kar- riereoptionen hat. Das Individuum kann zwischen einer mittleren Manage- mentposition in einer großen Firma und einer leitenden Position in einer kleineren börsennotierten Gesellschaft wählen, in der es die Möglichkeit hat, den Wert der Aktie der eigenen Gesellschaft zu beeinflussen. Das Individuum investiert in den Finanzmarkt einschließlich der Aktie der kleineren börsen- notierten Gesellschaft. Die nutzenmaximierende Konsum-, Investitions- und Arbeitsaufwandsstrategie wird in geschlossener Form hergeleitet. Es werden Bedingungen in Form eines Einkommensunterschiedes angegeben, bei denen das Individuum die Karriere in der kleineren börsennotierten Gesellschaft fortführt. Diese kann ein geringeres Einkommen anbieten. Das Einkommens- defizit wird durch die Möglichkeit, von einem gesteigerten Arbeitsaufwand durch Ankauf von eigenen Firmenaktien zu profitieren, kompensiert. Diese Ergebisse geben einen Einblick in das optimale Design von Verträgen

Four Generations of Asset Pricing Models and Volatility Dynamics

The scope of this diploma thesis is to examine the four generations of asset pricing models and the corresponding volatility dynamics which have been devepoled so far. We proceed as follows: In chapter 1 we give a short repetition of the Black-Scholes first generation model which assumes a constant volatility and we show that volatility should not be modeled as constant by examining statistical data and introducing the notion of implied volatility. In chapter 2, we examine the simplest models that are able to produce smiles or skews - local volatility models. These are called second generation models. Local volatility models model the volatility as a function of the stock price and time. We start with the work of Dupire, show how local volatility models can be calibrated and end with a detailed discussion of the constant elasticity of volatility model. Chapter 3 focuses on the Heston model which represents the class of the stochastic volatility models, which assume that the volatility itself is driven by a stochastic process. These are called third generation models. We introduce the model structure, derive a partial differential pricing equation, give a closed-form solution for European calls by solving this equation and explain how the model is calibrated. The last part of chapter 3 then deals with the limits and the mis-specifications of the Heston model, in particular for recent exotic options like reverse cliquets, Accumulators or Napoleons. In chapter 4 we then introduce the Bergomi forward variance model which is called fourth generation model as a consequence of the limits of the Heston model explained in chapter 3. The Bergomi model is a stochastic local volatility model - the spot price is modeled as a constant elasticity of volatility diffusion and its volatility parameters are functions of the so called forward variances which are specified as stochastic processes. We start with the model specification, derive a partial differential pricing equation, show how the model has to be calibrated and end with pricing examples and a concluding discussion