Probabilistic and analytic methods for pricing American style of Asian options
Tomáš Bokes
PhD thesis advisor: Daniel Ševčovič
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Summary: In the thesis, we analyze floating strike American style Asian options with various averaging and lookback options. As one of the main results, we present a new unifying method for calculation of the limit of early exercise boundary at expiry. The method can be used for any financial derivative that can be transformed into a so called Doob-Meyer decomposition of Snell envelope of its discounted pay-off function. Results for the limit of early exercise boundary of American style of option strategies calculated by this approach are compared to results calculated by the PSOR method. The early exercise boundary of analyzed options is estimated by the first order of polynomial expansion. We use the condition of smoothness of solution to derive the expansion close to expiry. The result is consistent with already known values derived for plain vanilla options. In the thesis, we also present a differential equation for the early exercise boundary of analyzed options. This equation is derived from the modification of Black-Scholes partial differential equation.
Related papers

[1] T. Bokes and D. Sevcovic, Daniel: Early Exercise Boundary for American Type of Floating Strike Asian Option and Its Numerical Approximation, Applied Mathematical Finance, 2011 DOI:10.1080/1350486X.2010.547041
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[2] T. Bokes, Valuation of the American-style of Asian option by a solution to an integral equation, Acta Universitatis Matthiae Belii ser. Mathematics, 16 (2010), 17-23.
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[3] T. Bokes, The Early Exercise Boundary behavior at expiry for American style of derivative, submitted 2011,
arXiv: 1012.0348