Contributions published at Financial Engineering (Markus Leippold)

We propose a new modeling framework to study the asset pricing implications of learning under ambiguity aversion. In a continuous time partial information Lucas economy, we characterize analytically equilibrium equity returns and make the following observations. First, learning under ambiguity aversion implies an equilibrium discount for ambiguity, if and only if relative risk aversion is below one or, equivalently, the elasticity of intertemporal substitution (EIS) is above one. In this case, ambiguity aversion increases conditional equity premia and volatilities. Second, equilibrium interest rates are lower, irrespective of risk aversion. Third, no time-invariant relation between excess returns and conditional variances exists. Therefore, estimated relations between excess returns and equity conditional variances are highly time varying and have an indeterminate sign. Fourth, estimates of the EIS based on standard Euler equations for equity returns are strongly downward biased in a setting of learning and ambiguity aversion. Therefore, an EIS well above one can be consistent with estimates of EIS well below one. Fifth, ambiguity does not resolve asymptotically. Finally, using realistic model parameters, we show that a low risk aversion and a moderate amount of ambiguity are consistent with the equity premium, the low interest rate, and the excess volatility puzzles.

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Both institutional and private investors often have only limited flexibility in timing their investment decision. They look for investments that will ideally be independent of the timing decision. In this article, a new class of derivative products whose payoff is linked to the trend of the underlying instrument is introduced. By linking the trend to the payoff, the timing of the decision becomes less important. Therefore, trend derivatives offer some time-diversification benefits. How trend derivatives are designed and priced is shown. Due to their peculiar features, trend derivatives offer some interesting applications such as executive stock option plans.

To simultaneously account for the properties of interest-rate term structure and foreign exchange rates within an arbitrage-free framework, we propose a multi-currency quadratic model with an (m+n) factor structure. The m factors model the term structure of interest rates in both countries. The n factors capture the portion of the exchange rate movement that is independent of the term structure of either country. We estimate a series of multi-currency quadratic models using U.S. and Japanese LIBOR and swap rates and the exchange rate between the two countries.

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Options whose payoff are linked to the trend of an underlying rather than to the underlying itself have many advantages, both for investors and hedgers. We describe the properties of trend options and show how the pin risk of these contracts is withdrawn.