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Distribution-Based Option Pricing On Lattice Asset Dynamics Models

Author

Listed:
  • YUJI YAMADA

    (Graduate School of Business Sciences, University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, Tokyo 112-0012, Japan)

  • JAMES A. PRIMBS

    (Management Science and Engineering, Stanford University, Terman Engineering Center 700-327, CA 94305-4026, USA)

Abstract

In this paper, we propose a numerical option pricing method based on an arbitrarily given stock distribution. We first formulate a European call option pricing problem as an optimal hedging problem by using a lattice based incomplete market model. A dynamic programming technique is then applied to solve the mean square optimal hedging problem for the discrete time multi-period case by assigning suitable probabilities on the lattice, where the underlying stock price distribution is derived directly from empirical stock price data which may possess "heavy tails". We show that these probabilities are obtained from a network flow optimization which can be solved efficiently by quadratic programming. A computational complexity analysis demonstrates that the number of iterations for dynamic programming and the number of parameters in the network flow optimization are both of square order with respect to the number of periods. Numerical experiments illustrate that our methodology generates the implied volatility smile.

Suggested Citation

  • Yuji Yamada & James A. Primbs, 2002. "Distribution-Based Option Pricing On Lattice Asset Dynamics Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(06), pages 599-618.
  • Handle: RePEc:wsi:ijtafx:v:05:y:2002:i:06:n:s0219024902001572
    DOI: 10.1142/S0219024902001572
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    Cited by:

    1. Anda, Jon & Golub, Alexander & Strukova, Elena, 2009. "Economics of climate change under uncertainty: Benefits of flexibility," Energy Policy, Elsevier, vol. 37(4), pages 1345-1355, April.

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