Impact of the inclusion of stochastic and conditional volatility of a commodity in real options valuation using the binomial options pricing model

Abstract

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.