Calibrated option bounds

The arbitrage-free interval gives bounds for the reasonable prices of a 
contingent claim in an incomplete market. In the approach of Ritchken and 
Kuo these bounds are computed numerically by solving two optimization 
problems over martingale measures for a discrete market model. It turns out 
that this approach is very sensitive to the choise of the model, 
and there is no general rule for choosing the right one. This paper shows how 
the available market information can be used to overcome this difficulty.  
Our approach is close to recently developed calibration approaches where the 
market information is used to pin down a particular pricing model that is 
consistent with observed security prices. An advantage of the present 
approach is that it relies less on user specified information and thus avoids 
problems with possible miss-specifications. Numerical tests on S&P500 options 
demonstrate the accuracy and robustnes of the method.