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Methodological Department

Self-consisted correlated evolution model

An industrial simulation needs for a huge amount of data, interest rate curves, foreign exchange rates, volatility surfaces, stock market prices, and a consistent methodology to efficiently consider mutual influence among all of them, in the way of a correlation structure.

An industrial simulation needs for a huge amount of data, interest rate curves, foreign exchange rates, volatility surfaces, stock market prices, and a consistent methodology to efficiently consider mutual influence among all of them, in the way of a correlation structure.

The correlation structure is especially problematic, since it needs for a detailed characterization of the financial instruments, through data market together with a calibration of an evolution model that holds the correlation structure itself. This approach, typically academic, allows a consistent calibration with data market. However, it lacks of flexibility enough to enclose a full simulation with multiple kinds of financial instruments.

In this work we have introduced an attempt of methodology where the correlation structure does not come from a calibration, but it is a solution from the evolution equations.

A historic correlation structure is mimic but in the future, those entries in the correlation matrix are unknown but can be calculated under certain assumptions self consistently. Although we show a very easy example restricted to two time steps, and two risk factors it is complex enough to illustrate the power of our approach, that hugely shrinks the dependence with external data, and allows an industrial attack of the problem.