Generalized Autoregressive Gamma Processes

We introduce generalized autoregressive gamma (GARG) processes, a class of autoregressive and moving-average processes that extends the class of existing autoregressive gamma (ARG) processes in one important dimension: each conditional moment dynamic is driven by a different and identifiable moving average of the variable of interest. The paper provides ergodicity conditions for GARG processes and derives closed-form conditional and unconditional moments. The paper also presents estimation and inference methods, illustrated by an application to European option pricing where the daily realized variance follows a GARG dynamic. Our results show that using GARG processes reduces pricing errors by substantially more than using ARG processes does.