Pricing of moving-average-type options with applications

✍ Scribed by Chih-Hao Kao; Yuh-Dauh Lyuu

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 200 KB
• Volume: 23
• Category: Article
• ISSN: 0270-7314
• DOI: 10.1002/fut.10072

✦ Synopsis

Abstract

Moving‐average‐type options are complex path‐dependent derivatives whose payoff depends
on the moving average of stock prices. This article concentrates on two such options traded in practice: the
moving‐average‐lookback option and the moving‐average‐reset option. Both options
were issued in Taiwan in 1999, for example. The moving‐average‐lookback option is an option struck
at the minimum moving average of the underlying asset's prices. This article presents efficient algorithms
for pricing geometric and arithmetic moving‐average‐lookback options. Monte Carlo simulation
confirmed that our algorithms converge quickly to the option value. The price difference between geometric
averaging and arithmetic averaging is small. Because it takes much less time to price the
geometric‐moving‐average version, it serves as a practical approximation to the arithmetic
moving‐average version. When applied to the moving‐average‐lookback options traded on
Taiwan's stock exchange, our algorithm gave almost the exact issue prices. The numerical delta and gamma of
the options revealed subtle behavior and had implications for hedging. The moving‐average‐reset
option was struck at a series of decreasing contract‐specified prices on the basis of moving averages.
Similar results were obtained for such options with the same methodology. © 2003 Wiley Periodicals, Inc.
Jrl Fut Mark 23:415–440, 2003