We compute a sharp small-time estimate for implied volatility under a general uncorrelated local-stochastic volatility model, with mild linear growth conditions on the drift and vol-of-vol. For this we use the Bellaiche\cite{Bel81} heat kernel expansion combined with Laplace's method to...

We study optimal buying and selling strategies in target zone models. In these models the price is modeled by a diffusion process which is reflected at one or more barriers. Such models arise for example when a currency exchange rate is kept above a certain threshold due to central bank...

In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and uniqueness of the solutions to such RBSDEs in appropriate...

We use probabilistic methods to characterise the optimal exercise region of a swing option with put payoff, $n\ge 2$ exercise rights and finite maturity, when the underlying asset's dynamics is specified according to the Black & Scholes model. The optimal exercise region of each right (except...

The intermarket analysis, in particular the lead-lag relationship, plays an important role within financial markets. Therefore a mathematical approach to be able to find interrelations between the price development of two different financial underlyings is developed in this paper. Computing the...

In an analysis of the US, the UK, and the German stock market we find a change in the behavior based on the stock's beta values. Before 2006 risky trades were concentrated on stocks in the IT and technology sector. Afterwards risky trading takes place for stocks from the financial sector. We...

The seniority of debt, which determines the order in which a bankrupt institution repays its debts, is an important and sometimes contentious feature of financial crises, yet its impact on system-wide stability is not well understood. We capture seniority of debt in a multiplex network, a graph...

This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of age pyramid which evolves according to immigration and...

Technical trading rules have a long history of being used by practitioners in financial markets. Their profitable ability and efficiency of technical trading rules are yet controversial. In this paper, we test the performance of more than seven thousands traditional technical trading rules on...

The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the interconnectedness of the system entities and the corresponding...