Three papers in Financial Risk Management

The presentation concerns numerical analysis of stochastic models for a fundamental question in risk management: how best to use financial derivatives. Although much is known about pricing derivatives and managing market risk, the analysis has novel aspects. First, I develop a model where an agent holds one unit of stock and buys some quantity of put option. I explore how the optimal amount of put options varies with preferences and relate results to insurance economics. Second, I calculate time and ensemble averages in different sample sizes, which shows the put-option model has non-ergodic properties. Third, I introduce an index derivative, where the agent buys a derivative on an index number with a statistical relationship to profit. I use a simulation experiment to show that larger statistical explanatory power does not necessarily ensure larger risk management power, what matters is the index number’s accuracy at predicting losses.