Contributions published at Financial Engineering (Markus Leippold)

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In a one-good one-period economy, I extend the classical capital asset pricing model by including skewness and kurtosis risk. Credit portfolios are characterized by negative skewness and fat tails (left- skewed and leptokurtic distribution), both of which must be priced according to Kimball’s (1993) concept of standard risk aversion. I explain the large increase in the credit default swap index prices, by decomposing the credit spread into physical and systematic risk be- fore and after the financial market crisis. The findings show that the increase was driven by both, a higher risk aversion of the default pro- tection seller and an increase of the physical default probabilities.

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We propose a combination of a Local Volatility model for equities with a Vasicek process for interest rates in order to price hybrid options via a PDE Finite Element Method. Under consideration of the interaction between stochastic interest rates and Local Volatility, and with particular attention to problems that arise when Local Volatility assumptions are violated, we derive the discretisation scheme needed for a numerical implementation of this model. We obtain arbitrage-free prices for a wide set of hybrid options, and infer an implied interest rate-equity correlation

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Credit risk has been an increasing area of interest over the past few years: Among the different forms of financial risks, sovereign risk has become recently one of the major concerns of investors and it is now essential to detect and assess sovereign vulnerabilities to prevent severe financial shocks. Estimating the ability of a country to service its foreign currency denominated debt is usually done by analyzing macroeconomists forecasts on the economic prospects of a country. Forecasts on exports, imports, budget expenditures, tax collection… are combined with accounting ratios (such as Debt to GDP) to assess the vulnerability of the sovereign. For corporates, two main categories of models have been developed to evaluate credit risk: Intensity based models and structural models. Intensity based models, which are based on an exogenous process describing the probability of default, are widely appreciated for their capacity to explain the market’s perception of default risk priced in credit derivative instruments. However, such models do not have the appealing economic interpretation of default that investors can find in structural models. Moreover, they cannot provide a coherent framework to price both equity and credit products or capture the information in other markets (equity, currencies…). Structural models are based on the analysis of an entity’s balance sheet to identify mismatches and quantify inherent uncertainties into risk indicators. This kind of models appeared with the famous “Merton’s model”. While the Merton’s model has been greatly improved by many extensions, research on structural models remained focused on corporate credit risk. Recent publications propose a sovereign balance sheet to apply the Merton’s model to credit risk. We will see how structural models combined with financial derivatives pricing techniques can be used to assess risk for sovereign bonds. As a first step, a balance sheet of a sovereign is proposed, based on the balance sheets of its government and central bank. A structural approach is then developed to determine the risk of foreign currency denominated bonds of a country. This approach is tested against market data for various countries and is finally applied for investment purposes. Finally a second and less specific approach is developed for Eurozone countries in distress by relying on credit derivatives markets.

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Despite the enormous growth of the asset management industry during the past decades, little is known so far about the asset pricing implications of investment intermediaries. Investment objectives of professional asset managers such as mutual funds differ from those of private households. However, standard models of investment theory do not address the distinction between direct investing and delegated investing. Our objective is to get a formal understanding of equilibrium implications of delegated asset management. In a model with endogenous delegation, we find that delegation under benchmarking leads to more informative prices, to a beta adjustment, and to significantly lower equity premia.

Naively testing for accruals mispricing in 26 equity markets - one market at a time - we find statistical evidence of anomalous returns in some countries. However, some of these findings might well be spurious because of data snooping biases that arise when simultaneously testing several hypotheses. While the accrual anomaly is not deemed to be robust in some countries when properly accounting for multiple testing we find the international momentum effect to by and large pass the battery of multiple testing procedures. Moreover, we find the few robust accrual anomalies vanishing in recent times indicating that investors have been exploiting the mispricing.

We find that price and earnings momentum are pervasive features of international equity markets even when controlling for data snooping biases. For European countries, we find that price momentum is subsumed by earnings momentum on an aggregate level. However, this rationale does not apply to each and every country. While the above explanation is confined to certain time periods in the U.S., earnings momentum nevertheless appears to be a crucial driver of the price momentum anomaly in many markets. Since we cannot establish a decent relation between momentum and macroeconomic risks, we suspect a behavioral-based explanation to be at work. In fact, we find momentum profits to be more pronounced for portfolios characterized by higher information uncertainty. Hence, the momentum anomaly may well be rationalized in a model of investors underreacting to fundamental news. Finally, we find that momentum works better when limited to stocks with high idiosyncratic risk or higher illiquidity, suggesting that limits to arbitrage deter rational investors from exploiting the anomaly.