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.

Dynamic Upper Leg Strength and Neuromuscular Function in Children, Adolescents and Adults

This study examined muscle strength, muscle performance, and neuromuscular function during contractions at different velocities across maturation stages and between sexes. Participants included pre-pubertal, late-pubertal and adult males and females. All completed 8 isometric and 8 isokinetic leg extensions at two different velocities. Peak torque (PT), rate of torque development (PrTD), electromechanical-day (EMD), rate of muscle activation (Q30), muscle activation efficiency and coactivation were determined. Sex, maturity, and velocity main effects were found in PT and PrTD, reflecting greater values in men, adults, and isometric contractions respectively. When values were normalized to quadriceps cross-sectional area (qCSA), there was still an increase with maturity. EMD decreased with maturity. Adults had greater activation efficiency than children. Overall, differences in muscle size and neuromuscular function failed to explain group differences in PT or PrTD. More research is needed to investigate why adults may be affected to a greater extent by increasing movement velocity.