The aim of this Master Thesis is to estimate the prices of one-month calendar spread call options on crude oil, employing a stochastic pricing model for the underlying Futures prices of this energy commodity and a Monte Carlo simulation based model. The consistency of the results from our estimations is tested and a comparison with observed market prices is performed, in order to evaluate the accuracy of the sequential implementation of the two models. We analyse the very particular commodity market, concentrating even more our efforts in the description of energy markets. Great attention is also given to the idiosyncratic characteristics of commodities prices: mean reversion, convenience yield, seasonality and jumps. We give particular emphasis to oil, the world’s most important commodity and the underlying commodity of the calendar spread options we are pricing. In this study, we implement a three-factor model developed by Cortazar and Schwartz (2003). This model accounts for mean reversion and for the existence of convenience yield, while the other two characteristics of commodities prices are not included. In the same study, the authors proposed a technique to estimate the model parameters that is an alternative to the more demanding Kalman filter. We deeply discuss the former approach and individuate its advantages and disadvantages. We implement this technique in order to find the values for the parameters that, according to the three-factor stochastic model suggested by the authors, describe the price behaviour of the light sweet crude oil. These findings are later used as an input in the option pricing model. Regarding the estimation of the parameters and Futures prices our findings suggest a mean reversion coefficient for the convenience yield that is higher than the one found in previous studies. We also obtained a level of the demeaned convenience yield volatility that is lower than the one we expected. The correlation between the spot price and the price appreciation of crude oil is also too low, which is usually not a characteristic of this market. The correlation between the convenience yield and the spot price is high and positive, which support the mean reversion of crude oil price. These results were then used in the Monte Carlo simulation model built to price one-month calendar spread options. Despite a correct implementation of the model, our estimates turned out to be excessively low compared to the prices observed in the market. To understand the reason of this mispricing we perform a sensitivity analysis and we compute, according to our model, the implied values of some pricing parameters. Low values for state variables volatilities and correlations seem to be the drivers of the underestimation of our option prices.
|Educations||MSc in Finance and Strategic Management, (Graduate Programme) Final Thesis|
|Number of pages||140|