Real-world barrier options are almost never continuously monitored — exchange-traded barrier options are monitored at discrete fixing times (daily close, or even intraday), and OTC contracts use daily or weekly observations. The difference between continuous and discrete monitoring is not negligible: a discretely monitored barrier that "almost" touches the barrier level between fixings survives, while a continuously monitored barrier would have knocked out.
This lesson quantifies the discrete monitoring adjustment (the Broadie-Glasserman-Kou correction) and introduces the Parisian option, which requires the stock to remain above (or below) the barrier for a minimum duration before the knock-out or knock-in activates — a smoothed version of the standard barrier that is more robust to "barrier hunting."
Learning objectives. By the end of this note you should be able to:
- state the Broadie-Glasserman-Kou correction formula and apply it to a discretely monitored DO call;
- define the Parisian option and explain its economic motivation;
- describe qualitatively how discrete monitoring affects the knock-out probability.
In this lesson
- 4.1 Continuous vs discrete monitoring
- 4.2 The Broadie-Glasserman-Kou correction
- 4.3 Parisian options
Before you start
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