Probabilistic and analytic methods for pricing American style of Asian options
PhD thesis advisor:
PhD thesis - Full text (PDF 11 MB)
Synopsis (PDF 611 KB)
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.
 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
 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.
 T. Bokes, The Early Exercise Boundary behavior at expiry for American
style of derivative, submitted 2011,