In this dissertation it was described in detail the multiplicative quadrinomial tree numerical
method with nonconstant volatility, based on a basis a proposal system of stochastic
differential equations. The methodology allowed to estimate first, the value of the parameters
based on an estimate conditional volatility process for a WTI oil commodity prices quoted in
the Bloomberg platform, then they were derived and found their equivalent parameters in the
proposed stochastic differential equations system, and finally the appropriate numerical
method was constructed to include the volatility that was estimated. For the above, the first
two moments of the proposed equations were derived to estimate the respective
recombination between discrete and continuous processes and, as a result, a numerical
methodological proposal was formally presented to value, with relative ease, both real and
financial options, when the volatility was stochastic. The main findings showed that when in
the proposed method the volatility approached to zero, the multiplicative binomial traditional
method was a particular case, and that the results were comparable between these
methodologies, as well as with the exact solution offered by the Black-Scholes model;
Finally, the originality of the methodological proposal was that it allowed for the emulation in
a simple way the presence of a nonconstant volatility in the price of the underlying asset, and
it could be used to value all kinds of options both for a real world and in risk-neutral
situations.
| Identifer | oai:union.ndltd.org:PUCP/oai:tesis.pucp.edu.pe:20.500.12404/13834 |
| Date | 27 March 2019 |
| Creators | Pareja, Julian A. |
| Contributors | Tuesta, Vicente |
| Publisher | Pontificia Universidad Católica del Perú, PE |
| Source Sets | Pontificia Universidad Católica del Perú |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/closedAccess |
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