Jun 28th, 2015
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A. T. Still University
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In this chapter, the analytic solution, Monte Carlo simulation, nite di erence method, and binomial tree model are introduced to price barrier options. Next, a fast and ecient method to price barrier options based on the re ection principle is introduced. Moreover, the method to price Parisian option is presented. Finally, other applications of barrier options are shown.

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Ch 8. Barrier OptionI. Analytic Pricing Formula and Monte Carlo SimulationII. Finite Difference Method to Price Barrier OptionsIII. Binomial Tree Model to Price Barier OptionsIV. Reflection Principle and Pricing Barrier OptionsV. Parisian Option PricingVI. Other Applications of Barrier Options Barrier options are path dependent options, but the dependence is weak because we onlyhave to know whether or not the barrier has been triggered during the option life. Anyother information associated with the path is not necessary to price barrier options. In this chapter, the analytic solution, Monte Carlo simulation, finite difference method,and binomial tree model are introduced to price barrier options. Next, a fast and efficientmethod to price barrier options based on the reflection principle is introduced. Moreover,the method to price Parisian option is presented. Finally, other applications of barrieroptions are shown.I. Analytic Pricing Formula and Monte Carlo Simulation There are closed-form solutions for pricing European-style barrier options. For instance,the pricing formula of the down-and-in call is as follows.cdown-and-in = S0 eqt (B/S0 )2 N (y) Kert (B/S0 )22 N (y T ),where =rq+ 2 /2,22/(S0 K)]y = ln[B+T,TB is the barrier level and assumed to be lower than the initial stock price. For the 8 types of barriersthe combinations of down or up, in or out, and call or put,t

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