Contributions published at Quantitative Finance (Erich Walter Farkas)

We investigate the Diffusion Operator Integral method initially proposed by Heath and Platen, allowing for variance reduced estimation of option prices using approximating payoffs- and model dynamics. We combine the method with the Longstaff-Schwartz algorithm for approximating optimal stopping time solutions in pricing problems for American options in an extension of the Heston stochastic volatility model. A generalization of Black-Scholes is used as an approximating model within this framework to capture the deterministic mean reversion components in this extended Heston model. We confirm the dramatic variance reduction results from previous research for our extension to the more complex stochastic volatility setting, while also extending applications of the method to American options.

We investigate the Diffusion Operator Integral method initially proposed by Heath and Platen, allowing for variance reduced estimation of option prices using approximating payoffs- and model dynamics. We combine the method with the Longstaff-Schwartz algorithm for approximating optimal stopping time solutions in pricing problems for American options in an extension of the Heston stochastic volatility model. A generalization of Black-Scholes is used as an approximating model within this framework to capture the deterministic mean reversion components in this extended Heston model. We confirm the dramatic variance reduction results from previous research for our extension to the more complex stochastic volatility setting, while also extending applications of the method to American options.

The 2008 financial crisis showed that various approaches for monitoring risk within financial institutions demonstrated weaknesses. To address this, the stress testing framework has been strengthened, with a greater focus from the regulators’ side. Along with ad-hoc scenarios generated to assess the health of banks under stress, financial institutions have the possibility to develop alternative approaches yielding improved stress estimates. This project focuses on a statistical scenario generation methodology, which produces a wide set of plausible stress scenarios. We propose a methodology which assesses their similarity and determines representative scenarios, which are then leveraged for new simulations. In order to obtain a distribution of the representative scenario, the importance sampling algorithm is applied. Such an approach falls in the category of reverse stress testing.

In this thesis, a new dynamic, multi-period portfolio optimization framework is proposed. Specifically, this framework is tailor-made for a hypothetical investor with respect to four key factors: a) the time horizon of the investment, b) the risk profile of the investor, c) the final and intermediate wealth goals of the investor, and d) the cashflows from the investor. In con- trast with classical single-block approaches to portfolio optimization, we propose a three-step solution that allows an investor to observe and take active part in the decision-making process. Taking the investor’s specifications into account, the proposed optimization procedure finds the optimal dynamic portfolio strategy that maximizes the probability of achieving all wealth goals cumulatively. We introduce various means of visualization of both the intermediate steps and final outputs, with the aim of better understanding the optimization process. The core of the framework is the dynamic programming algorithm proposed by Das et al. (2018a). By reviewing the theory of dynamic programming, we extend the algorithm by introducing new features in the model, such as intermediate wealth goals.

The objective of this thesis is to investigate the possibility of using structural credit risk models in the context of CVA calculations with wrong-way risk in the electricity market. The modelling approach can be divided into two major steps. It first derives the unconditional dynamic credit exposures for energy forward contracts with a specic delivery pattern (physical "flow-delivery" within a pre-defined delivery interval) as well as for plain vanilla options on such forward contracts. The derivation builds on the underlying forward curves simulated according to an extension of the three-factor model in the sense of [Bjerksund et al.], which is based on the well-known HJM framework [Heath, Jarrow, and Morton]. A multi-period Merton-type structural credit risk model then is applied to introduce default scenarios for the credit exposure profiles by using a joint Monte Carlo simulation. In particular, the methodology is able to take wrong-way/right-way risk into account for CVA calculations on all hierarchical levels of the portfolio/netting sets and could also be applied for credit portfolio risk calculations with wrong-way/right-way risk.

This thesis investigates the option pricing performance of the Black-Scholes and Heston models. The Heston model assumes the underlying stock’s volatility to be stochastic rather than constant during the option contract’s life. Both models were tested using S&P 500 index call options. The Heston model first had to be calibrated using a non-linear optimization technique. The calibration process provided a quick solution, and the Heston model prices were calculated. The analysis indicates that the Heston model outperforms the Black-Scholes model. The Heston model can explain the implied volatility phenomena better. However, for short-lived, deep-in-the-money and deep-out-of-the money options, the Heston model is quite error prone. The pricing accuracy increases with the time to maturity. Nevertheless, one can conclude that stochastic volatility models are inevitable in option pricing and that the Black-Scholes model should only be used as a benchmark model. Models more sophisticated than the Heston model can provide even better results.

This thesis examines a Risk Parity Approach on the Swiss Financial Market in which each investment in the portfolio contributes the equal amount of risk to the overall portfolio risk. Four investment strategies are cross-checked: the value-weighted market portfolio, a 60/40 portfolio, an unlevered Risk Parity portfolio and a levered Risk Parity portfolio. This approach was able to generate a higher return than the traditional benchmark portfolios in the ten years since the financial crisis in 2008 to 2017. If, however, realistic assumptions are integrated into the calculation, such as a realistic borrowing rate and thus costs of leverage as well as transaction costs, the excess return declines very sharply and one is far from finding statistical significance for the excess returns. The selection of the asset class, the method for measuring the risk of an asset or the period under consideration can have a substantial influence on the result of the investment strategy relative to the comparable portfolios. Thus, based on the results of this study, it is not appropriate to argue that the Risk Parity Approach is fundamentally superior.

In recent years, it has become clear that an isolated micro-prudential approach to capital adequacy requirements of individual institutions is insufficient. It can increase the homogeneity of the financial system and ultimately the cost to society. For this reason, the focus of the financial and mathematical literature has shifted towards the macro-prudential regulation of the financial network as a whole. In particular, systemic risk measures have been discussed as a risk mitigation tool. In this spirit, we adopt a general approach of multivariate, set-valued risk measures and combine it with the recently proposed notion of intrinsic risk measures. In the latter, instead of using external capital to define the risk of a financial position, we use internal capital, which is received when part of the currently held position is sold. We translate this into a systemic framework and show that the systemic intrinsic risk measures have desirable properties such as monotonicity and quasi-convexity. Furthermore, for convex acceptance sets we derive dual representations of the systemic intrinsic risk measures.

A new foreign currency hedging strategy for international investors is motivated and studied. Model-free optimal foreign currency exposures for a risk averse investor are derived. Based on those, and assuming a very flexible non-Gaussian returns model for currency and portfolio returns, we build a dynamic currency hedging strategy. In the context of our model, each element of the vector return at time $t$ is endowed with a common univariate shock, interpretable as a common market factor. It is shown that this mixing random variable plays the role of ambiguity (uncertainty about the return distribution), where its magnitude is expressed through the size of the market factor's conditional variance. Using the derived theoretical model and the proposed dynamic hedging strategy, an out of sample back test on the historical market data is performed. The results show that the approach yields a robust and highly risk reductive hedging strategy, obtainable with low transaction costs.

The choice of optimal currency exposure for a risk and ambiguity averse international investor is derived and studied. Robust mean-variance preferences, explicitly capturing investor’s dislike for model uncertainty, are used in order to derive the model-free optimal currency exposure in the presence of both risk and ambiguity aversion. Additionally, we show that the sample efficient currency demand is found as a vector of generalized ridge regression coefficients of fully hedged portfolio returns on excess currency returns, where the model uncertainty corresponds to the penalty term in the regression. The empirical analysis of the currency hedging strategy is conducted using the foreign exchange, stock, and bond returns over the period 1999 to 2018. We find that the proposed hedging strategy leads to significant improvements of the portfolio performance and examine the effect of model uncertainty on equilibrium currency allocations.

The choice of optimal currency exposure for a risk and ambiguity averse international investor is derived and studied. Robust mean-variance preferences, explicitly capturing investor’s dislike for model uncertainty, are used in order to derive the model-free optimal currency exposure in the presence of both risk and ambiguity aversion. Additionally, we show that the sample efficient currency demand is found as a vector of generalized ridge regression coefficients of fully hedged portfolio returns on excess currency returns, where the model uncertainty corresponds to the penalty term in the regression. The empirical analysis of the currency hedging strategy is conducted using the foreign exchange, stock, and bond returns over the period 1999 to 2018. We find that the proposed hedging strategy leads to significant improvements of the portfolio performance and examine the effect of model uncertainty on equilibrium currency allocations.

During the 2008 global nancial crisis deterioration in the creditworthiness of a counterparty was a major source of losses for the banks, exceeding in many cases losses arising from outright defaults. This highlighted the importance of hedging against counterparty credit risk, particularly when it is correlated with mark-to-market losses. CVA (Credit Valuation Adjustment) is a model that was designed to capture this risk by measuring the difference between true portfolio value (that takes into account the possibility of a counterparty's default) and the risk-free portfolio value. Under the nalised version of the Basel III Accord, which is expected to take effect in 2022, the revised CVA framework offers a more risk-sensitive approach by taking into account the market risks that affect the exposures and their associated hedges. The new framework replaces the Standardized Method (SM) and Current Exposure Method (CEM) with the new Standardized Approach (SA-CCR) for calculating EAD. Firms with no regulatory approval for Internal Model Method (IMM) can calculate CVA by using the Basic Approach (BA-CVA) and the SA-CCR component. For rms with IMM approval there is the choice to use either the basic approach or the standardized one (SA-CVA). The aim of the thesis will be to compare CVA charges under these different cases for a given portfolio and for different stress scenarios. The portfolio consists of OTC derivatives, and particularly Interest Rate and Foreign Exchange Swaps, which make up the majority of derivatives market.

Financial capital markets usually are assumed to be efficient, meaning that the prices fully reflect all available information. However, some studies have reported mixed results, with many arguing against the efficient markets theory in markets worldwide. This thesis investigates whether or not several different calendar anomalies exist within the Swiss Performance Index, namely the Day of the Week Effect, the Weekend Effect, the Friday the 13th Effect, the January Effect, the Mark Twain Effect and the January Barometer. It uses the Welch’s t-test and the Ordinary Least Squares regression methodology in order to examine this. The findings indicate that there is no Day of the Week Effect associated with any weekday within the index. Furthermore, the results also show that the Weekend Effect, the Friday 13th Effect, the January Effect and the Mark Twain Effect do not exist in the Swiss Performance Index. Additionally, the January Barometer appears to have no significant predictive power within the index. These conclusions indicate that the Market Efficiency Theory does - in regards to the examined calendar anomalies - hold true for the Swiss Performance Index.

A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram–Charlier series expansion, known as the Gauss–Hermite expansion. This expansion converges for fat-tailed distributions commonly encountered in the study of financial returns. The expansion coefficients can be calibrated from observed option prices and can also be computed, for example, in models with the probability density function or the characteristic function known in closed form. We investigate the properties of the new option pricing model by calibrating it to both real-world and simulated option prices and find that the resulting implied volatility curves provide an accurate approximation for a wide range of strike prices. Based on an extensive empirical study, we conclude that the new approximation method outperforms other methods both in-sample and out-of-sample.

The IASB introduced IFRS 9 as a direct response to the criticism that the incurred loss methods of accounting resulted in banks recognising loan losses too little, too late during the financial crisis. IFRS 9 has been adopted since 1 January 2018 and one of its central changes is the migration to an expected credit loss (ECL) approach. This paper attempts to provide a timely answer to some important questions worrying investors and regulators as a result of the standard's non-prescriptive requirements. Probability of default models required for lifetime ECL calculations under multiple economic scenarios are presented on a large dataset observing mortgages between 2000 and 2018. Criteria and thresholds for assessments of significant increase in credit risk, which inform the need for 12-month or lifetime provisioning, are discussed. By focusing on practical considerations, key challenges and some of the approaches observed in the industry, this paper also attempts to bridge a potential gap between auditors and credit risk experts.

Over the past few years, the cryptocurrency market experienced very high volatility prices, which has attracted scholars to analyze and anticipate this market. Nowadays, there exist more than 2000 different digital coins, among which Bitcoin is the most famous one. Since the level of returns and volatilities in the stock market are lower than those of the cryptocurrency market, in this article, we try to find some new risk measures. The goal of this research is by using time series analysis and some statistical methods, such as statistical process control, extreme values theory and loss distribution approach to estimate loss distribution of some cryptocurrencies which have the highest rate of capital in the whole market, in particular, Bitcoin, Ethereum, and Ripple. To do that, we need to first, review the pricing models which can be applied to the digital coins. The next step is stylized facts about these coins. Then, we have to define and compare different measures of risk. These can be obtained by estimating the loss distribution and time series analysis. Next, we can discuss whether these risk measures are capable of being applied to the stock market or not. To verify that idea, we made a portfolio and optimized it in several different ways. We used three main risk measures such as Standard Deviation, Value at Risk and Expected Tail Loss. Then, by using obtained weights, we constructed a new portfolio and used future data set. Deriving the return of each portfolio proved which risk measure works better in this context. Relation and dependencies are another essential part of this research. We applied different correlations, such as Distance correlation and rank correlations, and also copula to discover the relations between different markets, gold, USD index, S&P 500 and S&P GSCI for instance. Since we are dealing with several indices, we combined all three coin into one index. Also, we used change-point detection to separate time in three main periods. In the end, we made some applications of Extreme Value Theory and find out which coin is riskier.

This thesis shows how token issuers can overcome information asymmetry by successfully signalling relevant investment information, such as quality of application, product, team and company or credibility signals to subscribers and investors. The academic literature on ICO success criteria is still heavily geared towards 2017 ICO data. Only few publications already extend to Q1/2018 or even Q2/2018 data. This analysis confirms major results of the empirical research based on the statistical analysis of 2018 data for the Swiss and the Liechtenstein ICO market. The study includes 145 Swiss and 7 Liechtenstein ICOs completed in 2018 and 28 different success criteria. The analysis confirms the paramount importance of the disclosure of quality (Source code on GitHub, ICObench.com rating) and of the disclosure of credibility (i.e., incorporation of the issuer), besides the power of social media marketing. It also confirms the “wisdom of the crowd” effect.

As extreme value theory has been rapidly developed over the past several decades, many scholars have explored its applications on the stock market and insurance. However, little light has been shed on the money market. This thesis contributes to expanding the study target to the money market and examines whether the interest rate behavior can also be captured by the extreme value models. The underlying risks of the interest rate movement are estimated using a self-calibrating method and then compared with other extreme value models. The thesis also aims to investigate the extreme risks in interest rate by exploring the probability of large movements.

The subject of this work is the study of the determinants of the Italian NPL stock and the analysis of the resolutions. When determining the driver of the distressed credit stock a panel data analysis on 11 listed banks for the period 2001-2017 has been applied. The fixed effect estimation highlighted that both macroeconomic and bank-specific variables concur in determining the NPL ratio level. The NPL market is characterised by informational asymmetries that result in a pricing gap between banks net book value and market evaluation of NPL. The lack of a well functioning secondary market for distressed credit coupled with economy downturn contributed to the build up of a EUR 350 billion stock of non performing loans in the Italian banking system. In order to reduce the amount of NPL both public measures and private initiatives have been undertaken. From the government side the set up of an asset protection scheme for senior securitised tranches of NPL (GACS) and law reforms regarding judicial proceedings and collateral enforcement have been adopted. When it comes to the first, an estimation of the potential costs for the State has been carried out based on a modelling of the portfolio losses and it turned out that the resources funded by the government are indeed adequate to cover the average loss on securitised tranches. From the private side the inception of Atlante funds was undertaken in the attempt to reduce the bid-ask spread and foster the NPL transactions. Both public and private measures contributed to the development of the Italian NPL market that was characterised by a frency activity and jumbo deals starting from 2017. Consequently, after years of constant increase, the Italian NPL stock started to reduce in size, with such a trend expected to continue for 2018. Pricing gap on the Italian market still persist and will force credit institutions to face losses when disposing of their distressed credit thus putting preassure on banks’ capitalization. At the same time, the entering into force of the new IFRS standards with respect to asset classification and provisioning will further reduce the CET ratio of Italian credit institutions. As highlighted by an analysis of the Italian banking sector, the massive NPL stock is considered to be the main cause of the low profitability and of the credit crunch affecting the economy in the last years, with the Italian GDP growth that, since the outburst of the great financial crisis, has been below the EU average. NPL resolution will take some time and will require strong efforts from the both the private and the public sector, but it is expected to positively contributed to economy recovery.

The current thesis provides a valuable comparison between Basel III/IV and Solvency II in a qualitative as well as quantitative level. The thesis is mainly concentrated on Pillar 1 quantitative capital requirements for both regulatory frameworks. A comparison of the standard approaches for market and credit risk of Basel III/IV and Solvency II takes place in the quantitative analysis of this thesis. The results indicate considerable differences between the two regulatory frameworks that could potentially lead to regulatory arbitrage opportunities. The analysis starts with the comparison of the banking and insurance industry and ends up with comments/concerns regarding the future of financial regulation.