Contributions published at Financial Engineering (Markus Leippold)

We study the intra-horizon value at risk (iVaR) in a general jump diffusion setup and propose a new model of asset returns called displaced mixed-exponential model, which can arbitrarily closely approximate finite-activity jump-diffusions and completely monotone Levy processes. We derive analytical results for the iVaR and disentangle the risk contribution of jumps from diffusion. Estimating the iVaR for several popular jump models using on S&P 100 option data, we find that option-implied estimates are much more responsive to market changes relative to their historical counterparts. Moreover, disentangling jumps from diffusion, jump account for about 90 percent of iVaR on average.

null

null

null

We consider real-world modelling of foreign exchange (FX) markets with multiple currencies under the benchmark approach. We model the respective numeraire portfolio under multiple currency denominations using a multi-currency minimal market model, and derive FX rates by ratios of these denominations. We use an approximation to the numeraire portfolio by a well diversified world savings account index and fit the model using historical exchange rate and savings account data. We then compute real-world pricing of European call options on FX rates using the fitted model. We further consider hedging strategies of the call option under benchmarked risk minimization, and compare the hedging errors with delta hedging strategies.

null

null

null

This bachelor thesis looks at how various measures of stock-performance in Switzerland can be predicted, using firm-specific, categorised newspaper article counts and past financial market data. The period of analysis is 2008 to 2013. Future stock performance is being explained with the help of regression models, whose output is made further use of in the designing of investment strategies, with which to acquire significant risk-adjusted returns whose size outperforms those gained with the help of classic financial analysis tools, such as the Capital Asset Pricing Model (CAPM). The use of news-data in this context has turned out to be moderately useful.

As an alternative for the ”standard” Dividend Growth Model (Gordon Growth Model) with implied exponential dividend growth, this thesis introduces a ”modified” Dividend Growth Model by Balschun and Schindler (2015) with implied linear dividend growth. Standard portfo- lio construction techniques are applied to test whether the models can be exploited successfully in terms of risk-adjusted excess returns within the Swiss stock market. After considering trans- action costs, significant annualized alphas of over 10% are being measured for portfolios based on the ”modified” Dividend Growth Model. The outcomes vary over time and depend on the chosen measures for the variables within the Dividend Growth Models.

null

Monte Carlo simulations represent an easy and generic valuation method for the pricing of option derivatives. But the statistical error related to the simulation mechanism possesses a slow convergence rate of order O(1/√n). This thesis provides an overview of variance reduction techniques increasing the efficiency of Monte Carlo methods without increasing the number of sample paths n. In particular, the focus is set on a comparison between a multilevel Monte Carlo setting using a multigrid discretization with different lengths of time steps, and a quasi-Monte Carlo setting using either a randomized rank-1 lattice rule or a scrambled Sobol low-discrepancy sequence as pseudorandom number generator for the Brownian increments. The implementation part presents a numerical simulation study which includes the pricing of a Lipschitz-continuous European option, a strongly path-dependent lookback option, and a barrier option with discontinuous payoff across three market models (Black-Scholes’ GBM, Heston’s stochastic volatility and Merton’s jump-diffusion). For basket options, the study includes the assessment of Sobol numbers based on a Brownian bridge interpolation which is known to be an efficient dimension reduction technique for quasi-Monte Carlo integration. The results show that for options written on a single underlying, quasi-Monte Carlo does not provide any improvement of the estimate’s convergence rate, regardless of payoff structure and market model. The multilevel algorithm computes fast and accurate price estimates. For basket options without the multilevel treatment, we observe the curse of dimensionality impairing the quality of Sobol numbers over the unit hypercube, but its efficiency is partially restored by replacing the Cholesky factorization with a Brownian bridge. For a Lipschitz- continuous European payoff, a multilevel quasi-Monte Carlo setting combined the strengths of both variance reduction methods and provided a price estimate faster than each method on its own.

null

We analyze the impact of funding costs and margin requirements on index options traded on the CBOE. Assuming differential borrowing and lending rates, we derive no-arbitrage bounds for European options. We show that funding costs and the CBOE’s margin requirements lead to a price increase, which translates into skew and smile patterns for implied volatility curves even under constant volatilities. Empirical tests confirm that our model-implied slopes have significant statistical power in explaining the slopes observed in the market. Hence, at least in part, funding costs and collateral requirements offer an institutional explanation of the volatility smile phenomenon.

null

The pricing of options is an important topic in modern financial markets. Empirical findings show that sophisticated models rather than standard Black Scholes model are more adequate to reproduce the reality on option markets. In this thesis the characteristics of the Black Scholes, the Heston, the Merton and the Bates model are discussed and compared with traded options on the Swiss Market Index. Particularly the Bates model can cope best with the empirical findings. To price European option under such a stochastic volatility jump diffusion model the use of numerical methods is required. For this purpose the Monte Carlo simulation, numerical integration and Fast Fourier transform are chosen and analyzed in detail. To render a comparison of the different techniques possible, an option pricing application is developed. Advantages, disadvantages, limitations and performance of these methods are assessed and discussed. Finally, a recommendation on the choice of the most suitable method to price regular European options under a stochastic volatility jump diffusion model is given.

null

null

This thesis analyses the suitability of portfolio optimisation based on Polynomial goal program- ming (PGP) and Omega Ratio, respecting constraints faced by Swiss pension fund investors. 10 time series with 802 weekly data points each from 2000 to 2015 are used to assess risk and estim- ate co-moments, applying shrinkage estimators. 20 returns sets are simulated, using Johnson-SU - distributions and Efficient Frontiers are repeatedly estimated for PGP and Omega Ratio as well as for mean-variance and CVaR optimisation for comparative purposes. The procedure leads to Omega efficient portfolios, outperforming the other methodologies with respect to holistic performance meas- ures looking at the entire distribution, such as Omega or Sortino Ratios. However, the procedure performs weakly for PGP, mean-variance and CVaR optimisation. The outcome further suggests that analysing individual moments is not appropriate to assess portfolio risk.

Es hat sich herausgestellt, dass trotz teilweise mangelnder Transparenz und gesellschaftlicher Akzeptanz von Securities Lending und Borrowing (SLB)-Geschäften an einen Finanzmarkt ohne SLB nicht zu denken ist. Wenn das Gegenparteirisiko durch eine sorgfältige Auswahl determiniert wird, eine adäquate Collateralization erfolgt und die vertragliche Ausgestaltung Wirksamkeit und Durchsetzbarkeit garantiert, ist das Risiko eines SLB-Geschäfts auf besicherter Basis im Grundsatz als gering zu beschreiben. Wird diese Erkenntnis im Vergleich zu den zahlreichen Nutzen des SLB betrachtet, liegt der Schluss nahe, dass dieser Geschäftstyp als zweckmässig, vielfältig einsetzbar und darüber hinaus unverzichtbar für das effiziente und stabile Funktionieren heutiger Finanzmärkte beschrieben werden kann.