Korn–Kreer–Lenssen model

The grain - Kreer - Lenssen model ( KKL model) is a discrete trinomial model, which was introduced in 1998 by Ralf Korn, Markus Kreer and Mark Lenssen for modeling illiquid shares or securities prices. It generalizes the binomial Cox-Ross- Rubinstein model in a natural way by the stock at a discrete point in time either rises, falls or remains unchanged. The model can thus be used to determine the fair value of option prices. In contrast to the Cox-Ross- Rubinstein model, the market is here originally not yet complete and the duplication principle needed for dynamic replication of the option next to the stock and the risk-free money market account another with the stock " related " securities, such as a low exercise price option (short LEPO ) to complete the market. The mathematical proof of arbitrage freedom is based on Martingale representations of point processes, which were formulated in the 1980s and 1990s by mathematicians Albert Nikolaevich Shiryaev, Robert Liptser and Marc Yor.

The dynamics of the KKL model based on linear birth and death processes, can specify for which explicit solution formulas. Later work concerned with the completion of the market through call and put options with any strike price and the valuation of exotic options.