Contributions published at Financial Engineering (Markus Leippold)

We study the optimal policies and mean-variance frontiers (MVF) of a multiperiod mean-variance optimization of assets and liabilities (AL). This makes the analysis more challenging than for a setting based on purely exogenous liabilities, in which the optimization is only performed on the assets while keeping liabilities fixed. We show that, under general conditions for the joint AL dynamics, the optimal policies and the MVF can be decomposed into an orthogonal set of basis returns using exterior algebra. This formalism, novel to financial applications, allows us to study analytically the structure of optimal policies and MVF representations under endogenous liabilities in a multidimensional and multiperiod setting. Using a numerical example, we illustrate our methodology by analysing the impact of the rebalancing frequency on the MVF and by highlighting the main differences between exogenous and endogenous liabilities.

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This paper performs specification analysis on the term structure of variance swap rates on the S&P 500 index and studies the optimal investment decision on the variance swaps and the stock index. The analysis identifies two stochastic variance risk factors, which govern the short and long end of the variance swap term structure variation, respectively. The highly negative estimate for the market price of variance risk makes it optimal for an investor to take short positions in a short-term variance swap contract, long positions in a long-term variance swap contract, and short positions in the stock index.

We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with nonunique quantiles, thereby extending the work of Feldman and Tucker. We illustrate the algorithm with an example from credit portfolio risk analysis.

This paper concerns the pricing of American options with stochastic stopping time constraints expressed in terms of the states of a Markov process. Following the ideas of Menaldi et al., we transform the constrained into an unconstrained optimal stopping problem. The transformation replaces the original payoff by the value of a generalized barrier option. We also provide a Monte Carlo method to numerically calculate the option value for multidimensional Markov processes. We adapt the Longstaff-Schwartz algorithm to solve the stochastic Cauchy-Dirichlet problem related to the valuation problem of the barrier option along a set of simulated trajectories of the underlying Markov process.

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Am 1. Januar treten die neuen Anlagerichtlinien für Schweizer Vorsorgeeinrichtungen in Kraft. Mit ihnen dürfte die Professionalisierung der zweiten Säule weiter vorangetrieben werden. Der Anpassungsbedarf bei den Vorsorgewerken ist unterschiedlich.

We introduce a new class of flexible and tractable matrix affine jump-diffusions (AJD) to model multivariate sources of financial risk. We first provide a complete transform analysis of this model class, which opens a range of new potential applications to, e.g., multivariate option pricing with stochastic volatilities and correlations, fixed-income models with stochastically correlated default intensities, or multivariate dynamic portfolio choice with volatility and correlation jumps. We then study in more detail some of the new structural features of our modeling approach in two applications to option pricing and dynamic portfolio choice. First, we find that a three-factor matrix AJD model can generate variations of the implied volatility skew term structures that are largely unrelated to the level and composition of the spot volatility. This feature can allow the model to improve on benchmark AJD settings in reproducing the overall shape of the smile of equity index options. Second, we find that volatility and correlation jumps can imply an economically relevant intertemporal hedging demand in optimal dynamic portfolios, when jump intensities exhibit co-movement with the returns’ covariance.