This paper utilized the proposed historical simulation, where the effect of GARCH (1,1) model on price path were considered, and the Monte Carlo approach were also used to examine the difference in option payoff values between these simulation approaches and the original path. Furthermore, we showed which simulation model would have smaller root mean squared pricing error by examining the difference of root mean squared pricing error between these approaches. We applied these approaches to simulate option payoff values on the Shenzhen composite index series in China during the period 2005 to 2009, and the common back-testing approach was used. The results showed that the estimated option values were significant and differ from the actual Shenzhen composite index option payoff values for the observed period. Finally, we found that the root mean squared pricing error of the adjusted historical simulation is less than the other two simulation approaches.
Key words: Simulation approaches, option payoff values, GARCH, valuation, price paths.
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