Contributions published at Quantitative Finance (Erich Walter Farkas)

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In this work we explore the implications of cointegration in a system of commodity prices on the premiums of options written on various spreads on the futures prices of these commodities. We employ a parsimonious, yet comprehensive model for cointegration in a system of commodity prices. The model has an exponential affine structure and is flexible enough to allow for an arbitrary number of cointegration relationships. We conduct an extensive simulation study on pricing spread options. We argue that cointegration creates an upward sloping term structure of correlation, that in turn lowers the volatility of spreads and consequently the price of options on them.

The values of options on realized variance are significantly impacted by the discrete sampling of realized variance and may be substantially higher than the values of options on continuously sampled variance (or, quadratic variation). Under arbitrary stochastic volatility dynamics, we analyze the discretization effect and obtain a simple analytical correction term to be applied to the value of options on continuously sampled variance. Our final result is remarkably compact and allows for a straightforward implementation in many of the standard stochastic volatility models proposed in the literature.

In this paper we propose a closed-form pricing formula for European basket and spread options. Our approach is based on approximating the risk-neutral probability density function of the terminal value of the basket using a Gauss-Hermite series expansion around the Gaussian density. The new method is quite general as it can be applied for a basket with a large number of assets and for all dynamics where the joint characteristic function of log-returns is known in closed form. We provide a simulation study to show the accuracy and the speed of our methodology.

The following paper proposes a portfolio performance measure to optimize, mostly bond asset portfolios usually held for regulatory purposes from a risk focused perspective. The measure is based on variations of the proximity measure introduced by the Random Forests framework, leading to a proximity based performance ratio. The proximities are modeled using a recursive conditional partitioning type of Random Forests, which allows for a ranking as well as an analysis of the risk drivers of the portfolio performance. The proximity based performance ratio is shown to, on average, outperform nine different and commonly known risk and performance ratios as well as the 1/N-balanced portfolio in three different tests, in- and out of the sample. The proximity based performance ratio can consider a large amount of risk rivers and is suitable for big data analysis for big and small financial institutions.

The importance of Cybersecurity has increased dramatically over the past few years. The frequency of cyber-attacks and data breaches seems to be constantly increasing with both companies and governments being affected. Extensive and periodic studies (especially in the United States and United Kingdom) provide insights into company awareness of cyber risks and how they are handled. However, these kinds of questions have been largely unexplored in Switzerland. Given the high global interconnectedness of Swiss companies and the im-portance of data privacy in many of Switzerland’s most important industries (especially the banking industry), these questions must be addressed. An anonymous survey of 92 Swiss companies and detailed interviews with 11 Swiss IT secu-rity professionals was conducted as part of this thesis. This effort was able to answer several of these questions. Although Swiss firms, in general, report that they are concerned about Cybersecurity, a sizeable percentage of companies still seem to lack appropriate awareness. The assessment of the employed defense measures was conducted through a comparison with best practice recommendations (compiled through an extensive literature review). The results indicate that Swiss firms, while doing reasonably well in certain areas, still have considerable room for improvement. With regard to cyber insurance the Swiss market is growing and be-coming more mature. However, it is still relatively underdeveloped with low coverage among Swiss companies (who have many reservations). In addition to these general findings, the thesis also provides detailed analysis of the observed differences among companies with different characteristics. It offers a basic Cybersecurity benchmark for Swiss firms, allowing them to compare themselves with their peers as well as against best practice methods.

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Any solvency regime for financial institutions should be aligned with the two fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. From these objectives wederive two normative requirements for capital adequacy tests, called surplus and numeraire invariance, respectively. We characterize capital adequacy tests that satisfy surplus and numeraire invariance, establish anintimate link between these requirements, and highlight aninherent tension between the ability to meet them and the desire to give credit for diversification.

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Financial markets of various asset classes have seen an increasing transition to orderdriven markets in recent years. Considering the greater transparency of the limit order book over simple information on best prices available in quote-driven markets, the assumption that this extended insight into the order book might contain some predictive content follows naturally. The literature however is not in absolute agreement about which aspects are relevant in explaining price movements or if there is a signicant relationship at all. This thesis addresses the question of whether the information contained within a limit order book regarding quoted interest and actual trades can help explain the future evolution of the mid price. For this purpose, a broad set of measurements to describe the state of the order book and information on trades therein is proposed and an empirical analysis using data from a major foreign exchange interbank market is conducted. An empirical strategy is employed that builds the forecasting model for the mid price returns endogenously from the most informative variables provided to the procedure. Analysis of the models selected by the strategy reveals that the features of the order book selected as informative predictors are consistent with the broader literature on limit order books. However, the empirical results obtained from these models cannot conrm signicant predictability of mid price returns. In contrast, the analysis identies that the information from the limit order book helps explaining the direction of very short-term price movements. These ndings are consistent across the evaluated currency pairs and forecast horizons. The thesis concludes that while mid price returns seem dicult to predict, a directional forecast for the very short-term is possible to some extent. This could be interpreted that that the limit order book in fact conveys some predictive content, which is however not fully identied by the constructed models.

In this thesis we discuss the wrong way risk of credit value adjustment (CVA) and debit value adjustment (DVA) for energy derivatives. After presenting and calibrating a forward price model for the electricity, oil and coal markets we concentrate on the models proposed by Brigo et al. (2009a), Hull and White (2012) and Rosen and Saunders (2012) which all allow for a dependence of exposures and default probabilities. For each of these models we propose and apply calibration methods using historical CDS spread and energy futures market data. This allows to calculate the CVA of randomly generated portfolios with 9 companies active in the energy market. We nd that the three models generally agree on the answer to the question if a portfolio contains right or wrong way risk and show highly correlated results, but they do not always agree on the exact level. We also nd that right/wrong way risk is less pronounced in the electricity market than in the oil market, which we attribute to lower historical dependence between forward prices and default probabilities of electricity companies than of oil companies, lower volatility observed in the electricity forward market and nally to the special payment terms of electricity forward contracts. Due to the large model risk revealed by these three models, the decision of the Basel Committee to consider wrong way risk using a rather conservative  factor seems to be justiable. We additionally nd that both a short and a long call option on the same electricity forward contract with the same counterparty can exhibit right way risk in all of these models, an observation which was not expected by intuition but can again be explained by the payment conditions of electricity forward contracts.

In the last years, following the nancial crisis from 2008, dierent ideas have been developed and implemented how to stabilize the banks and the banking system in general. One approach is the strengthening of the capital basis of the banks through issuing contingent convertible bonds (CCB or CoCo's), that in case of trouble convert from liabilities to equity through a dened triggering event. CCB should oer a long term protection to banks, similar to a long term insurance policy, that covers rare events with a certain threshold. They should also oer an investment opportunity to institutional investors in the times of low interest rates. The current work looks through the methods of Monte Carlo simulation into two particular details of the functioning of contingent convertible bonds (CCB's): the long term pricing and long term protection. One main result is that there is possibly an optimal issuing term from the point of view of the issuer, that in the discussed model is around 50 years for a CCB with conversion ratio of 0. The second main result is, that the frequency of default conditional on previous conversion is constant in time, and as expected lower for a high trigger than for a low one.

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