Applications of Malliavin Calculus to Derivatives Pricing within a Multi-curve BGM Framework

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Title: Applications of Malliavin Calculus to Derivatives Pricing within a Multi-curve BGM Framework
Author: Tapanainen, Niko
Contributor: University of Helsinki, Faculty of Science, Department of Mathematics and Statistics
Publisher: Helsingin yliopisto
Date: 2018
Language: eng
Thesis level: master's thesis
Discipline: Applied Mathematics
Soveltava matematiikka
Tillämpad matematik
Abstract: The past decade has brought about two key changes to the pricing of interest rate products in the European fixed income markets. In 2007, the Euribor-EONIA spread widened, which called into question the use of Euribor rates as a proxy for the risk-free rate. Nine years later, all of the main Euribor rates had fallen below zero. These changes forced market practitioners to reassess their assumptions, which resulted in the development of new models. The Heath-Jarrow-Morton (HJM) and Brace-Gatarek-Musiela (BGM) frameworks, which had gained popularity before the crisis, have served as a foundation for these models. In this thesis, we present two applications of Malliavin calculus to the pricing of interest rate derivatives within a multicurve BGM framework. Although the framework simplifies the pricing of interest rate derivatives, as it takes market rates as primitives, the pricing of exotic interest rate derivatives can pose a number of problems. The complexity of these products can lead to situations that require the use of computational techniques such as Monte Carlo simulation. This, in turn, provides an opening for the application of Malliavin calculus. We end this thesis by presenting a Malliavin-based formula for the price and the delta-sensitivity of a snowball, and discuss the merits of these representations in the context of Monte Carlo simulation. With reference to advances within the field during the last 5 years, we discuss the possible developments within the field that might garner further interest towards Malliavin calculus in the near future.

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