Year of publication
- Zinsstrukturmodelle : Hedging im Hull/White-Einfaktormodell in diskreter und stetiger Zeit (2004)
- Der Beitrag beschäftigt sich mit dem Hull/White-Einfaktormodell und diskutiert Aspekte der Bewertung von Zinsderivaten sowie des Hedgings in diskreter und stetiger Zeit. Es stellt sich zunächst heraus, dass sich die Preise von Derivaten im von Hull/White vorgeschlagenen diskreten Bewertungsalgorithmus und die Preise in stetiger Zeit für sehr kleine Zeitschritte (fast) entsprechen. Ein Nachteil des diskreten Modells ist, dass - anders als beispielsweise im Binominalmodell von Cox/Ross/Rubinstein - keine selbstfinanzierende Handelsstrategie existiert, mit deren Hilfe die Preise eines risikoneutralen Investors "erzwungen" werden können. Dieses Problem besteht jedoch nicht mehr bei der Modellbetrachtung in stetiger Zeit. Die im diskreten Modell geschätzten Hedgeratios approximieren die theoretischen Werte für kleine Zeitschritte recht gut. So gesehen ist der Hull/White-Trinominalbaum als Instrument zu interpretieren, mit dessen Hilfe Zinsderivate, für die keine analytischen Bewertungsformeln existieren, unter der Annahme des zeitstetigen Shortrate-Prozesses bewertet und gehedged werden können. Der Artikel schließt mit der Herleitung von Hedgeratios zur Steuerung des Modellrisikos ab.
- Where Should You Buy Your Options? : The Pricing of Exchange-Traded Certificates and OTC Derivatives in Germany (2006)
- 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.
- Trading Strategies with Partial Access to the Derivatives Market (2010)
- 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.
- The New Basel Capital Accord (2005)
- This paper addresses the capital requirements based on the RiskMetrics™ framework and the BIS standard model. A case study is developed which shows that the capital requirements can be reduced by applying the more accurate RiskMetrics™ framework. Furthermore it gives an overview of the capital requirement rules for credit risk and operational risk in the Basel II Accord.
- Spread ladder swaps - an analysis of controversial interest rate derivatives (2012)
- 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.
- Risk-Neutral Densities and Catastrophe Events (2012)
- 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.
- Pricing Turbo Certificates in the Presence of Stochastic Jumps, Interest Rates, and Volatility (2007)
- Keep on smiling? The pricing of Quanto options when all covariances are stochastic (2012)
- 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.