The pricing of options on an interval binomial tree. An application to the DAX-index option market

This paper implements a model setup in Muzzioli and Torricelli [Int. J. Intell. Syst. 17 (6) (2002) 577-594] for deriving implied trees and pricing options when the put-call parity is not fulfilled. The model basically extends Derman and Kani's [Risk 7 (2) (1994) 32-39], whereby call (put) prices are also used in the lower (upper) part of the tree thus exploiting the information content of both call and put prices. The DAX-index option market is chosen for this application because it is a relatively new European market where short-selling restrictions may induce put-call parity violations and the nature of the option (European) and of the underlying (dividends reinvested in the index) avoid some estimation problems. In order to test the pricing fit of the model, a non-linear optimisation procedure is proposed to estimate a unique implied tree which allows a comparison between the model prices, Derman and Kani's and market prices. The results suggest that the MT model improves the pricing.