ICCS 2001: Computational Science — ICCS 2001 pp 579-588 | Cite as
Construction of Multinomial Lattice Random Walks for Optimal Hedges
Conference paper
First Online:
Abstract
In this paper, we provide a parameterization of multinomial lattice random walks which take cumulants into account. In the binomial and trinomial lattice cases, it reduces to standard results. Additionally, we show that higher order cumulants may be taken into account by using multinomial lattices with four or more branches. Finally, we outline two synthesis methods which take advantage of the multinomial lattice formulation. One is mean square optimal hedging in an incomplete market and the other involves pricing under “implied volatility” and “implied kurtosis”.
Keywords
Option Price Implied Volatility Incomplete Market Local Volatility Binomial Tree
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Download
to read the full conference paper text
References
- 1.Bellman, R.: Dynamic Programming. Princeton University Press, Princeton, NJ (1957)Google Scholar
- 2.Black, F., Scholes, M.; The Pricing of Options and Corporate Liabilities. Journal of Political Economy 81 (1973) 637–654CrossRefGoogle Scholar
- 3.Bouchaud, J-P. and M. Potters.: Theory of Financial Risks. Cambridge University Press (2000)Google Scholar
- 4.Cox, J. C., Ross, S. A.: The valuation of options for alternative stochastic processes. Journal of Financial Economics 3 (1976) 145–166CrossRefGoogle Scholar
- 5.Cox, J. C., Ross, S. A., Rubinstein, M.: Option pricing: A simplified approach. Journal of Financial Economics 7 (1979) 229–263CrossRefMATHGoogle Scholar
- 6.Derman, E., Kani, I.: Riding on a Smile. Risk 7 (1994) 18–20Google Scholar
- 7.Fedotov, S., Mikhailov, S.: Option Pricing for Incomplete Markets via Stochastic Optimization: Transaction Costs, Adaptive Control, and Forecast. Int. J. of Theoretical and Applied Finance 4 No. 1 (2001) 179–195CrossRefMathSciNetMATHGoogle Scholar
- 8.J. Hull, Options, Futures, and Other Derivative Securities, 4th edition. Englewood Cliffs: Prentice-Hall, 1999.Google Scholar
- 9.Hull, J., White, A.: The Pricing of Options on Assets with Stochastic Volatilities. Journal of Finance 42 (1987) 281–300CrossRefGoogle Scholar
- 10.Jarrow, R., Rudd, A.: Approximate option valuation for arbitrary stochastic processes. Journal of Financial Economics 10 (1982) 347–369CrossRefGoogle Scholar
- 11.Jarrow, R., Rudd, A.: Option Pricing. McGraw-Hill Professional Book Group (1983)Google Scholar
- 12.Karandikar, R. L., Rachev, S. T.: A generalized binomial model and option pricing formulae for subordinated stock-price processes. Probability and Mathematical Statics 15 (1995) 427–447MATHMathSciNetGoogle Scholar
- 13.Merton, R. C., Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3 (1976) 125–144CrossRefMATHGoogle Scholar
- 14.Pirkner, C. D., Weigend, A. S., Zimmermann, H.: Extracting Risk-Neutral Densities from Option Prices Using Mixture Binomial Trees. Proc. of the IEEE/IAFE/INFORMS Conf. on Computational Intelligence for Financial Engineering (1999) 135–158Google Scholar
- 15.Potters, M., R. Cont and J-P. Bouchaud.: Financial markets as adaptive systems. Europhys. Lett. 41 No. 3 (1998) 239–244CrossRefGoogle Scholar
- 16.Rubinstein, M.: Implied Binomial Trees. Journal of Finance 3 (1994) 771–818CrossRefGoogle Scholar
- 17.Rubinstein, M.: On the Relation Between Binomial and Trinomial Option Pricing Models. Research Program in Finance Working Papers, #RPF-292, University of California at Berkeley (2000)Google Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2001