Pricing of Some Path-Dependent Options on Equities and Commodities

Abstract: This thesis brings together three papers about the pricing of European and Bermudan path-dependent options, and one paper about the stochastic modelling of a futures price curve. Paper one proposes a fast numerical method to compute the price of so called cliquet options with global floor, when the underlying asset follows the Bachelier-Samuelson model. These options often constitute the option part of many capital guaranteed products, and are slow to price with existing Monte Carlo and PDE methods. Paper two deals with the pricing of swing options, when the logarithm of the underlying asset follows an Ornstein-Uhlenbeck process driven by a jump diffusion. Swing options are Bermudan or American options with multiple exercise rights, and are common on the energy markets. Paper three investigates the valuation of a natural gas storage facility, when gas trading is permitted on the spot- and futures markets simultaneously. The main idea is to interpret the storage as a swing option and then apply option pricing methods. Paper four proposes, estimates and evaluates two classes of parsimonious models of the correlation matrix for natural gas futures returns. The individual futures prices follow a Bachelier-Samuelson model with time-dependent volatility.