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Callable swaps, snowballs ans videogames

Claudio Albanese (Imperial College, University of London)

In this paper, we argue that the paradigm shift toward GPU architectures currently taking place in the high performance computing world can potentially change the situation and tilt the balance back in favour of a new generation of short rate models. We find that operator methods provide a natural mathematical framework for the implementation of realistic short rate models that match features of the historical process such as stochastic monetary policy, calibrate well to liquid derivatives and provide new insights on complex structures. The talk gives an introduction to the technical operator methods underlying this work such as the use of fast exponentiation, smoothing, Abelian processes, moment methods and dynamic conditioning. We then show that callable swaps, callable range accruals, CMS spreads, target redemption notes (TARNs) and various flavours of snowballs and snowblades can be priced with methods numerically as precise, fast and stable as the ones based on analytic closed form solutions by means of BLAS level-3 methods on massively parallel GPU architectures.

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