The …xed rate tender is one of the main operational formats usedby central banks in the implementation of their monetary policies. Whileacademic research has largely dismissed the procedure for its tendency to en-courage overbidding, central banks such as the ECB and the Bank of Englandhave...

We provide a new method to derive the state price density per unit probabilitybased on option prices and GARCH model. We derive the risk neutraldistribution using the result in Breeden and Litzenberger (1978) and thehistorical density adapting the GARCH model of Barone-Adesi, Engle, andMancini...