TY - JOUR T1 - In-Out Parity Relations for American-Style Barrier Options JF - The Journal of Derivatives SP - 20 LP - 32 DO - 10.3905/jod.2016.23.4.020 VL - 23 IS - 4 AU - João Pedro Ruas AU - João Pedro Vidal Nunes AU - José Carlos Dias Y1 - 2016/05/31 UR - https://pm-research.com/content/23/4/20.abstract N2 - Like plain-vanilla calls and puts, barrier options feature an exercise price that determines the payoff at expiration, but also a second “in” or “out” strike. If the underlying stock price hits this barrier, an “in” option is “knocked in” and becomes like an ordinary European thereafter, but unless it is knocked in before expiration, the option expires worthless, regardless of the final stock price. An “out” option is knocked out and expires if the underlying stock price hits the barrier. There might be a fixed “rebate” paid when that happens. It is not hard to see that an “in” option plus an “out” option with the same strike add up to a regular European contract, because one and only one can be exercised. But this is not true if the options allow American exercise. The holder of the two contracts might choose to exercise the out contract just before the barrier is hit, but hold onto the “in” contract until the barrier is reached, thus getting paid on both the in and the out contracts. Ruas, Nunes, and Dias find a solution to this problem that leads to a modified version of in-out parity for American barrier options.TOPICS: Options, quantitative methods ER -