By Xingjian Xu
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Extra info for Fake Geometric Brownian Motion And Its Option Pricing
Similarly but with less clarity on the plot, the distribution of the path average via AY fake GBM has a higher centralized peak compared to the one under B&S setting, but with more downside average events which take place. For Asian options, we find that although the option prices are close for the three processes, the distributions of the path average are different. 6: Histograms of the path average for the three processes. 35 CHAPTER 4. 4 Variance swap A variance swap () is a contract with payoff at maturity [X]T − κvar , where Xt = ln(St /S0 ) and [X]t is the quadratic variation of (Xt ).
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S´eminaire de Probabilit´es XIII, Lecture Notes in Mathematics, Volume 721/1979:90–115, 1979.  L. Bachelier. Th´eorie de la sp´eculation. Annales Scientifiques de L’Ecole Normale Sup´erieure, 17:21–88, 1900.  S. Black and M. Scholes. The pricing of options and corporate liabilities. The Journal of Political Economy, Vol. 81, No. 3:637–654, 1973.  P. Glasserman. Monte Carlo Methods in Financial Engineering. Springer, 2003.  K. C. Klebaner. A family of non-gaussian martingales with gaussian marginals.