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ISBN 9783843904629

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978-3-8439-0462-9, Reihe Mathematik

Tilman Sayer
Valuation of American-style derivatives within the stochastic volatility model of Heston

139 Seiten, Dissertation Technische Universität Kaiserslautern (2012), Softcover, A5

Zusammenfassung / Abstract

In this thesis, we develop and employ a refined tree-based method for pricing financial derivatives in the stochastic volatility model of Heston.

A recursive formula to determine marginal and joint moments for the Heston model is derived and computational efficient trees for the variance and stock price processes are built. We focus on incorporating the correlation when the separate trees are joined and develop an optimization method to match against higher order mixed moments. We state numerical results for matching against both exact and linearized moments and employ an extrapolation method to further increase the pricing accuracy.

The valuation approach is employed to value employee stock options. Personal risk aversions of employees are incorporated into the model by maximizing expected utility. We extend the model to cover subjective market beliefs and derive theoretical results for several parameter constellations. A sensitivity analysis is performed for various parameters, covering a performance hurdle and the designated vesting period. We state optimal exercise frontiers.

A heuristic extension of the tree model is developed. With the purpose to further improve the pricing accuracy, we modify some correlation values incorporated in the tree. We derive three possible modifications and empirically compare them among themselves as well as with the base approach.

We find that our tree-based approximation approach for the stochastic volatility model of Heston is very well suited for pricing financial derivatives and outperforms existing approximation schemes.