Chapter 11. EXOTIC BARRIER OPTIONS

The following sections are included:INTRODUCTIONFLOATING BARRIER OPTIONSASIAN BARRIER OPTIONSFlexible Geometric Asian Barrier OptionsFlexible Arithmetic Asian Barrier OptionsFORWARD-START BARRIER OPTIONSPricing Forward-Start Barrier OptionsPresent Values of RebatesPricing Forward-Start Barrier Options in Closed-FormRebates of Forward-Start Barrier OptionsFORCED FORWARD-START BARRIER OPTIONSEARLY-ENDING BARRIER OPTIONSThe Density Function at MaturityA Unified Pricing Formula for Early-Ending Barrier OptionsVanilla OptionsDown-Out Vanilla Barrier Call OptionsDown-In Vanilla Barrier Call OptionsUp-In Vanilla Barrier Call OptionsPresent Values of Rebates for Early-Ending Barrier OptionsWINDOW BARRIER OPTIONSRebates for Window Barrier OptionsOUTSIDE BARRIER OPTIONSThe Unified Marginal Density FunctionThe Unified Pricing Formula for Outside Barrier OptionsVanilla Options As Special CasesVanilla Barrier Options As Special CasesThe Trivial Case of Zero CorrelationOUTSIDE ASIAN BARRIER OPTIONSCORRIDOR OPTIONSThe Density Function with Dual-Barriers and Definition of Corridor OptionsPricing Corridor Options Without RebatesThe Fourier Series Method to Price Corridor OptionsRebates of Corridor OptionsBARRIER OPTIONS WITH TWO CURVED BARRIERSSUMMARY AND CONCLUSIONSQUESTIONS AND EXERCISESQuestionsExercisesAPPENDIXDOUBLE INTEGRATION WITH BIVARIATE NORMAL DENSITY FUNCTIONSTHE DERIVATION OF THE UNIFIED DENSITY FUNCTION FOR EARLIER-ENDING BARRIER OPTIONSPROOF OF THE THREE IDENTITIESN2[A, B, 1] = M[min(A,B)]N2(A,B, −1) = 0, A + B ≤ 0N2(A, B, −1) =N[max(A, B)] − N[−min(A, B)], forA + B > 0THE DERIVATION OF THE UNIFIED DENSITY FUNCTION OUTSIDE BARRIER OPTIONSTHE DERIVATION OF THE PRICING FORMULA WITH FOURIER SERIESTHE DERIVATION OF THE PRESENT VALUES OF REBATES OF OUT-CORRIDOR OPTIONSAPPROXIMATING THE BIVARIATE NORMAL CUMULATIVE FUNCTION VALUESTo Express the Bivariate Function in Terms of Univariate FunctionsDrezner’s Approximations