Barrier Option Pricing Using Adjusted Transition Probabilities

MotivationNew ApproachResultsAdjusted Binomial (and Trinomial) TreeProcedureA Simple Example: Down-out call (DOC) with constant barrier (3)= Exit Probability. This is the probability that the assetprice, starting from S T0 and ending in S upT 0+δt, hits the barrierIn this case we have[ ( ) (pL δt (T 0, S T0 , S upT 0+δt, L) = exp − 2σ 2 δt ln S T0 Sup)]Tln0+δtL LpLδtWith this probability adjustment the price of the DOC nearthe barrier (when S downT 0+δt< L), at time T 0 , isC DOC = exp(−rδt)p up (1 − pL δt up)C(ST 0+δt)G. Barone-Adesi, N. Fusari, J. Theal Barrier Option Pricing Using Adjusted Transition Probabilities