The Economics of Time as it is Embedded in the Prices of Options

Risk neutral variance term structures are characterized by their time elasticities. They are synthesized by space scaling and time changing self decomposable laws at unit time. Monotone time elasticities are modeled using exponential functions while gamma functions permit humps. Results for both cases as time changes are followed by simultaneously space scaling and time changing. Space scaling contributes towards front end options while time changing works on the back end. Splitting the space scaling and time changing for the positive and negative moves delivers models with rising absolute skewness and kurtosis. The space scaled and time changed densities are those of additive processes made up by aggregating over time the space scaled innovations of the sum of two underlying time changed Lévy processes taken at log time. The space scaled process is also a space scaled solution to a time varying OU equation driven by a time changed Lévy process taken at log time, where the OU mean reversion rates are the time elasticities. The two processes are termed the space scaled and time change components and their relative contributions, space to time are determined to be twice the ratio of their variance elasticities