A stochastic dynamic programming approach for pricing options on stock-index futures

The aim of this thesis is to price options on equity index futures with an application to standard options on S&P 500 futures traded on the Chicago Mercantile Exchange. Our methodology is based on stochastic dynamic programming, which can accommodate European as well as American options. The model accommodates dividends from the underlying asset. It also captures the optimal exercise strategy and the fair value of the option. This approach is an alternative to available numerical pricing methods such as binomial trees, finite differences, and ad-hoc numerical approximation techniques. Our numerical and empirical investigations demonstrate convergence, robustness, and efficiency. We use this methodology to value exchange-listed options. The European option premiums thus obtained are compared to Black's closed-form formula. They are accurate to four digits. The American option premiums also have a similar level of accuracy compared to premiums obtained using finite differences and binomial trees with a large number of time steps. The proposed model accounts for deterministic, seasonally varying dividend yield. In pricing futures options, we discover that what matters is the sum of the dividend yields over the life of the futures contract and not their distribution.

Market reactions to changes in the Nasdaq-100 Index membership

We examine stock market reactions around the Nasdaq-100 Index reconstitutions. We find a symmetric and transitory price response accompanied by a significant increase in trading volume on the effective date. Firms added to the Nasdaq-100 Index experience significant increases in institutional ownership, the number of market makers, and the number of shareholders. In contrast, firms removed from the index show significant decreases in the number of institutional shareholders. Additions to the Nasdaq-100 Index also show significant increases in four liquidity measures, whereas deletions demonstrate significant decreases in two liquidity measures. These changes in liquidity are related to the abnormal return on the announcement day. Taken together, the results suggest support for the price pressure, liquidity, and investor awareness hypotheses.