Business, Legal & Accounting Glossary
Consider a knock-in call option with a strike price of EUR 100 and a knock-in barrier at EUR 110. Suppose the option was purchased when the underlier was at EUR 90. If the option expired with the underlier at EUR 103, but the underlier never reached the barrier level of EUR 110 during the life of the option, the option would expire worthless. On the other hand, if the underlier first rose to the EUR 110 barrier, this would cause the option to knock-in. It would then be worth EUR 3 when it expired with the underlier at EUR103.
In all, there are eight flavours of barrier options comprising European puts or calls having barriers that are:
Merton priced a down-and-out call option in his seminal (1973) paper. The classic paper providing analytic pricing formulas for barriers is Reiner and Rubinstein (1991). See Haug (1997) for an alternative treatment of the same formulas. A shortcoming of analytic formulas is their use of a single implied volatility. Because barrier options are path-dependent, it is desirable to model a term structure of implied volatilities. See Taleb (1996).
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This glossary post was last updated: 16th April, 2020 | 11 Views.