Korn–Kreer–Lenssen model (Ofer Abarbanel online library)

The Korn–Kreer–Lenssen model (KKL model) is a discrete trinomial model proposed in 1998 by Ralf Korn, Markus Kreer and Mark Lenssen[1] to model illiquid securities and to value financial derivatives on these.

It generalizes the binomial Cox-Ross-Rubinstein model in a natural way as the stock in a given time interval can either rise one unit up, fall one unit down or remain unchanged. In contrast to Black–Scholes or Cox-Ross-Rubinstein model the market consisting of stock and cash is not complete yet. To value and replicate a financial derivative an additional traded security related to the original security needs to be added. This might be a Low Exercise Price Option (or short LEPO). The mathematical proof of arbitrage free pricing is based on martingale representations for point processes pioneered in the 1980s and 1990 by Albert Shiryaev, Robert Liptser and Marc Yor.

References

  1. ^Korn, Ralf; Kreer, Markus; Lenssen, Mark (1998). “Pricing of european options when the underlying stock price follows a linear birth-death process”. Communications in Statistics. Stochastic Models. 14 (3): 647–662. doi:10.1080/15326349808807493.
  2. ^“Archived copy” (PDF). Archived from the original (PDF) on 2011-09-29. Retrieved 2011-06-21.
  3. ^http://resources.aims.ac.za/archive/2010/obeng.pdf[permanent dead link]

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