| Option pricing plays an important role in financial, energy, and commodity markets. The Black-Scholes model is an indispensable framework for the option pricing. This thesis studies the pricing of a swing option under stochastic volatility. A swing option is an American-style contract with multiple exercise rights. As such, it is an optimal multiple-stopping time problem. In this dissertation, we reduce the problem to a sequence of optimal single stopping time problems. We propose an algorithm based on the finite element method to value the option. In real-world applications, volatility is typically not a constant. Stochastic volatility models are commonly chosen for modeling dynamic changes of volatility. Here we use the finite element approach to handle this added complication and present numerical results. For benchmark comparisons, we develop Monte Carlo methods to simulate the swing option under stochastic volatility. We compare the results obtained from both approaches and demonstrate that the finite element method is accurate and efficient, whereas the Monte Carlo method is easy to implement. |
