Asian Perpetuities
| Název práce v češtině: | Asijské perpetuity |
|---|---|
| Název v anglickém jazyce: | Asian Perpetuities |
| Klíčová slova: | Asijské opce, perpetuity, Geometrický Brownův pohyb |
| Klíčová slova anglicky: | Asian options, perpetuities, Geometric Brownian motion |
| Akademický rok vypsání: | 2017/2018 |
| Typ práce: | diplomová práce |
| Jazyk práce: | angličtina |
| Ústav: | Katedra pravděpodobnosti a matematické statistiky (32-KPMS) |
| Vedoucí / školitel: | doc. RNDr. Jan Večeř, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 27.03.2018 |
| Datum zadání: | 03.04.2018 |
| Datum potvrzení stud. oddělením: | 19.04.2018 |
| Datum a čas obhajoby: | 04.02.2020 08:00 |
| Datum odevzdání elektronické podoby: | 06.01.2020 |
| Datum odevzdání tištěné podoby: | 06.01.2020 |
| Datum proběhlé obhajoby: | 04.02.2020 |
| Oponenti: | RNDr. Petr Čoupek, Ph.D. |
| Zásady pro vypracování |
| The aim of this thesis is to analytically characterize prices of perpetuities based on various averages (arithmetic, geometric or harmonic). These contracts can be called Asian perpetuities since the contracts on average prices are called Asian options. A classical result in this field is that the perpetual arithmetic average of a geometric Brownian motion has an inverse gamma distribution. The thesis should connect this fact with more recent advancements in the field, such as that the price of an Asian option admits a Black-Scholes representation and thus there is another martingale measure associated with the average asset as a numeraire. This measure is important for the hedging strategy of the Asian perpetuity. One should find the prices and hedges of all these contracts using both martingale methods and using methods of partial differential equations. |
| Seznam odborné literatury |
| Dufresne, Daniel. "An affine property of the reciprocal Asian option process." Osaka J. Math 38.2 (2001): 379-381.
Yor, Marc. "Bessel processes, Asian options, and perpetuities." Exponential Functionals of Brownian Motion and Related Processes. Springer Berlin Heidelberg, 2001. 63-92. Vecer, Jan. "Black–Scholes representation for Asian options." Mathematical Finance 24.3 (2014): 598-626. Vecer, Jan. "Asian options on the harmonic average." Quantitative Finance 14.8 (2014): 1315-1322. |