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Optimal Portfolio Choice, Derivatives and Event Risk (2013)
Matthias Muck Stefan Weisheit
Show/Hide Abstract Improving Discrete Implementation of the Hull and White Two-Factor Model (2005)
Matthias Muck Markus Rudolf
This research analyzes the convergence properties of a discrete implementation of the Hull and White two-factor model. It compares caplet prices using both the discrete valuation algorithm and the analytic solution. Quality of the results depends crucially on the properties of the model parameters. The valuation algorithm may be improved while preserving its computational efficiency. An application of the modified algorithm to the caplet pricing problem indicates that substantially reduced valuation errors.
Show/Hide Abstract Where Should You Buy Your Options? : The Pricing of Exchange-Traded Certificates and OTC Derivatives in Germany (2006)
Matthias Muck
With the expansion of electronic exchanges and the nearly universal access to the Internet, it has become possible for retail investors to buy and sell exchange-traded derivative contracts from their desktops. In Europe this ability has even been extended to allow small investors to purchase over-the-counter exotic option contracts through the Internet. In this article, Muck analyzes the pricing of a variety of web-traded exotic instruments, available in this „market.” As one would expect, the contracts are overpriced on average, relative to theoretical valuations based on exchange-traded options on the same underlying DAX index. A second hypothesis, that overpricing diminishes as the contracts approach maturity receives a little less support.
Show/Hide Abstract Locational Price Spreads and the Pricing of Contracts for Difference: Evidence from the Nordic Market (2009)
Jan Marckhoff Jens Wimschulte
In electricity markets, not only does the risk of substantial price variations over time exist, but so does the risk of price variations over space, as prices between locations can differ due to transmission congestion. To manage this risk, Contracts for Difference (CfDs), i.e., forwards on the spread between a particular area price and the (unconstrained) system price, were introduced at the Scandinavian electricity exchange Nord Pool at the end of 2000. We empirically investigate the pricing of these CfDs over the period 2001 through 2006 and find that CfD prices contain significant risk premia. Their sign and magnitude, however, differ substantially between areas and delivery periods, because areas are subject to transmission congestion to a varying extent. While the relation between risk premia and time-to-maturity is not uniform for CfDs, there is a negative relation for implied area and system forwards, which can be explained by the relative hedging demand of market participants. In addition, we find that risk premia of CfDs and implied area forwards vary systematically with the variance and skewness of the underlying spot prices. This confirms both implications of the Bessembinder and Lemmon [Bessembinder, H., Lemmon, M.L., 2002. Equilibrium pricing and optimal hedging in electricity forward markets. Journal of Finance, 57, 1347–1382] model.
Show/Hide Abstract A Robust Model of the Convenience Yield in the Natural Gas Market (2011)
Thomas Volmer
This study advances the research on the convenience yield of natural gas. Econometric models confirm that air temperature is an important explanatory variable in addition to storage levels. Furthermore, an extended linear model shows that one has to account for a changing cost of physical storage in the spirit of Brennan (1958). Besides this, an alternative regime-switching model for the convenience yield helps to put in perspective a prominent finding by Fama, and French (1987). That is, given binding capacity constraints for gas storage, the variance of the futures' basis will increase rather than decrease with the storage levels. Finally and most importantly, robustness tests demonstrate that the extended linear model produces the most viable forecasts and that these forecasts can help to amend the performance of reduced-form models for the gas spot price.
Show/Hide Abstract Trading Strategies with Partial Access to the Derivatives Market (2010)
Matthias Muck
This research analyzes tradingstrategies with derivatives when there are several assets and risk factors. We investigate portfolio improvement if investors have full and partialaccess to the derivativesmarkets, i.e. situations in which derivatives are written on some but not all stocks or risk factors traded on the market. The focus is on markets with jump risk. In these markets the choice of optimal exposures to jump and diffusion risk is linked. In a numerical application we study the potential benefit from adding derivatives to the market. It turns out that e.g. diffusion correlation and volatility or jump sizes may have a significant impact on the benefit of a new derivative product even if market prices of risk remain unchanged. Given the structure of risk investors may have different preferences for making risk factors tradable. Utility gains provided by new derivatives may be both increasing or decreasing depending on the type of contract added.
Show/Hide Abstract Keep on smiling? The pricing of Quanto options when all covariances are stochastic (2012)
Nicole Branger Matthias Muck
The paper introduces a model for the joint dynamics of asset prices which can capture both a stochastic correlation between stock returns as well as between stock returns and volatilities (stochastic leverage). By relying on two factors for stochastic volatility, the model allows for stochastic leverage and is thus able to explain time-varying slopes of the smiles. The use of Wishart processes for the covariance matrix of returns enables the model to also capture stochastic correlations between the assets. Our model offers an integrated pricing approach for both Quanto and plain-vanilla options on the stock as well as the foreign exchange rate. We derive semi-closed form solutions for option prices and analyze the impact of state variables. Quanto options offer a significant exposure to the stochastic covariance between stock prices and exchange rates. In contrast to standard models, the smile of stock options, the smile of currency options, and the price differences between Quanto options and plain-vanilla options can change independently of each other.
Show/Hide Abstract Spread ladder swaps - an analysis of controversial interest rate derivatives (2012)
Matthias Muck
This article analyzes spread ladder swaps traded by Deutsche Bank to several medium-size companies and municipalities. The value of these contracts is highly sensitive to correlations between forward rates. For a contract that was challenged by the medium-size company Ille at the Federal Court of Germany, it turns out that the derivative was originated at a negative market value of −90,000 to −115,000 euros (depending on the number of factors used in the model). Moreover, the model correctly predicts the range for the terminal payment after an adverse development of the term structure of approximately 567,000 euros. We also investigate a product feature that limits the upside potential from the viewpoint of the customer and show that it has a substantial impact on market values. According to the judgment handed down by the court, the bank should have informed the customer about the market value of the product in light of special circumstances. This raises questions as to which products must meet this requirement. Moreover, especially for exotic contracts, market prices are mostly model prices: for spread ladder swaps, substantially different prices are obtained even when investors agree on the variance/covariance matrix but disagree on the number of factors to apply in an implementation of a model.
Show/Hide Abstract Risk-Neutral Densities and Catastrophe Events (2012)
Michael Herold Matthias Muck
In this research, we analyze the impact of catastrophe events on riskneutral densities which can be implied from European option markets. As catastrophe events we consider the destruction of the nuclear power plant at Fukushima and the downgrading of U.S. sovereign debt in 2011. In an event study, we analyze the impact on European blue chip index options traded at EUREX. We find that after a short adaption period, probability mass of especially risk-neutral density functions derived from long-term options is shifted toward the right side. Thus, very good states of the economy become more expensive indicating higher prices for deep out-ofthe- money options. This signifies that there has been speculation on a recovery of the German stock market after the shocks.
Show/Hide Abstract Spot Price Models for Natural Gas - Robustness of the Convenience Yield Approach (2012)
Thomas Volmer
This thesis investigates spot price models for natural gas and develops a new model, which incorporates both the simplicity of the set-up of reduced-form models and economic insights into the most important drivers of gas prices. The model responds to common criticism on existing reduced-form models for energy prices, especially to certain misspecifications identified. More precisely, the stochastic convenience yield model by Gibson and Schwartz (1990) and Schwartz (1997), which has gained notable attention in practice, is extended by using a two-component convenience yield. The first component mirrors fundamental convenience yield dynamics, which arise from changes in air temperature and national gas inventories, whereas the second component represents changes in the risk attitude of market participants. With empirical data from the UK and US gas markets it is shown that the extended model significantly improves the out-of-sample price forecast with regard to the stochastic convenience yield model when the forecast horizon is increased beyond one day. At the same time, the in-sample and the cross-sectional fit to quoted futures prices along the term structure are at least as good as for the mentioned benchmark model. For both conceptual and numerical reasons, some further room for an amendment of the cross-sectional fit remains. Its realization would, however, necessitate a far more complex model set-up.

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