Korn-Kreer-Lenssen model
The Korn-Kreer-Lenssen model ( KKL model ) is a discrete trinomial model that was introduced in 1998 by Ralf Korn, Markus Kreer and Mark Lenssen to model less liquid stock or security prices. It naturally generalizes the binomial Cox-Ross-Rubinstein model , with the stock either rising, falling, or unchanged at some discrete point in time. 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 originally not yet complete and the duplication principle requires the option in addition to the share for dynamic replicationand the risk-free money market account another security "related" to the share, e.g. B. a Low Exercise Price Option (LEPO for short) to complete the market. The mathematical proof of freedom from arbitrage is based on martingale representations of point processes that were formulated in the 1980s and 1990s by mathematicians Albert Nikolajewitsch Schirjajew , Robert Liptser and Marc Yor .
The dynamics of the KKL model are based on linear birth and death processes , for which explicit solution formulas can be given. Later work deals with the completion of the market through calls or puts with any exercise price and with the valuation of exotic options.
literature
- Ralf Korn, Markus Kreer, Mark Lenssen: Pricing of european options when the underlying stock price follows a linear birth-death process. Stochastic Models Vol. 14 (3), 1998, pp. 647-662. ( PDF file for download)
- Xiong Chen: The Korn-Kreer-Lenssen Model as an alternative for option pricing. Willmott Magazine June 2004, pp. 74-80. ( PDF file )
Individual evidence
- ^ Xiong Chen: The Korn-Kreer-Lenssen Model as an alternative for option pricing. Willmott Magazine June 2004. pp. 74-80.