Méthodes numériques pour la valorisation d'options swings et autres problèmes sur les matières premières
- Geman, Hélyette
The thesis presents a construction of a grid that discretizes the threshold model introduced by Geman and Roncoroni (2006) for electricity spot prices, incorporating both mean reversion and jumps, the direction of the latter depending on the price of the underlying at the time of the jump. The grid is used for the pricing of derivatives of European style, by backward induction method, in a setting of both constant and time-changing parameters. Monte Carlo simulations confirm the accuracy of the grid method which in addition is a lot faster to run. The grid is also extended to a multi-layer framework for the pricing of swing options, of both storage and supply type, in the general case of time-changing parameters, where once again Monte Carlo simulations confirm the accuracy of the pricing results. The thesis ends with a study of the impact of commodity price returns to the returns of stock prices of companies that produce the relevant commodity (oil, copper and wheat are used in the study). The results provide evidence that the stock prices are indeed influenced by the price of the relevant commodity and that this influence has increased in recent years.
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