Publication at Faculty of Mathematics and Physics |
2008
Abstract
An application of the extended Kalman filtering methodology to arbitrage free SPD estimation shows that this method provides very good results for data sets with small number of distinct strike prices. When the number of distinct strike price increases, the linear model becomes overparameterized, the resulting SPD estimators are not smooth anymore and smooth SPD estimator is obtained by applying a kernel regression estimator allowing also calculation of pointwise asymptotic confidence intervals.
Compared to other commonly used estimation techniques, the extended Kalman filtering methodology is able to capture the intra-day development of the SPD and it allows to update the estimates dynamically whenever new information becomes available.