Liquidity risk estimation: Non-Gaussian AR models and quantile expansions

In the financial literature, prices are usually computed under hypotheses of no friction. "Liquidity" is one form of friction which has not received much attention until very recently. One important question which arises is how to incorporate liquidity into risks' computations. In this work I use the spread between bid and ask prices to answer this question. There are three main parts in this thesis. First, I argue that time series of the bid-ask spread follow an AR(1) model with non-Gaussian innovations and propose the use of some stochastic volatility models for the spread. Then I find quantile estimators for such models, obtaining an estimate of the "risk due to spread movements". Finally I derive an expansion for the quantile of the total losses which includes both the frictionless component plus a perturbation given by the spread. I include examples on how to compute such expansion for the models I proposed and also for models of the spread reported in the literature.