The scale of market shocks can be constructed in principle for any market: the indices are computed from the price time series. We computed the M for the foreign exchange market and each index S is associated to a currency pair. Then we derive from them an index per currency and an index for the whole market. Beside, we also measure the correlation between the SMS index and the size of the next price moves, showing a large correlation for short time intervals.
This is a first step towards building a Global Early Warning System for financial crises.
We derive a simplified form for the price of the passport option using local time. A key insight is that Tanaka's formula and the Skorokhod Lemma allow us to prove a direct relationship between the prices of passport and lookback options. Explicit calculations are provided in the case where the underlying is an exponential Brownian motion. A further issue in the analysis of passport options is the identification of the optimal strategy. The second contribution of this article is to extend existing results on the form of the optimal strategy from the exponential Brownian motion model to a wide class of alternative price processes. We achieve this using coupling arguments.
Some extensions to this model will be discussed, including asymmetric bounds on the position limit and some interesting price comparisons.
A toolbox is presented to compute and extract information from inhomogeneous time series, containing a large set of operators, mapping from the space of inhomogeneous time series to itself. These operators are computationally efficient (time and memory-wise) and suitable for stochastic processes. This makes them attractive for processing high-frequency data in finance and other fields. Using a basic set of operators, we easily construct more powerful combined operators which cover a wide set of typical applications.
Examples of operators are (exponential) moving averages, differentials, derivatives, moving norms, moving standard deviations, moving volatilities, etc. Some practical examples demonstrate the usefulness of these operators and their superiority in comparison to standard methods.
Ausgehend von einem durch Rootzén [1] erzielten Resultat werden wir Grenzwertsätze für empirische Prozesse herleiten, die auf den extremen Werten einer beta-mischenden Zeitreihe beruhen. Die in [2] entwickelten Methoden erlauben es dann, mit geringem Aufwand die asymptotische Normalität einer Vielzahl von aus der klassischen Extremwertstatistik wohlbekannten Schätzern nachzuweisen.
We consider the problem of determining recursively the conditional distribution of the state variable given the past observed asset prices; this has important implications for volatility estimation. For both price-jump models this leads to a nonlinear filtering problem with marked point process observations. We explain how this filtering problem can be solved via a computable approximation approach. We present results from a simulation study which analyzes the numerical and statistical properties of our approach. Time permitting we explain how this approach can be used in the determination of risk-minimizing hedging strategies.
The valuation theory presented seems to fill a gap between arbitrage valuation on the one hand and single agent utility maximization or full-fledged equilibrium theory on the other hand. "Coherent" valuation bounds strike a balance in that the bounds can be sharp enough to be useful in the practice of pricing and still be generic, i.e., somewhat independent of personal preferences, in the way coherent risk measures are somewhat generic.
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