Mathematics applied to finance: Regularities in the VIX and the distribution of option's payoff
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
This thesis presents three applications of Mathematics to Finance, from the empirical to the analytic level. The first part shows how the CBOE's market volatility index (VIX) has seasonal movements, using several statistical and econometrical tools. These tools complement each other. The application is shown in a way that illustrates how dangerous it is to apply only ordinary least squares methods to look for seasonality. The second part shows interesting patterns emerging from empirical distributions of S&P100 index (OEX) returns over some horizons conditioned to the VIX level. The third part shows the main features of the distributions of option's payoff obtained using mainly analytical tools. However, a computer is needed to get a general picture of the distribution useful for speculators and traders in isolation.