A note on the valuation of an exotic timing option

✍ Scribed by Bellalah, Mondher; Prigent, Jean-Luc

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 128 KB
• Volume: 17
• Category: Article
• ISSN: 0270-7314
• DOI: 10.1002/(sici)1096-9934(199706)17:4<483::aid-fut6>3.0.co;2-d

✦ Synopsis

This note compares the valuation of a "lookback" put option with that of an option which, at payoff, gives its holder the difference between the maximum value recorded during the option's life and an initial value based on underlying asset price at the time of initiation. This latter instrument is called an exotic timing option.

Although the payoff on the exotic option corresponds to a lookback option, a major advantage is that, in contrast to the lookback option, the holder does not run the risk of zero value when the maximum value is achieved at maturity. This note derives the value of an exotic option which gives its holder the difference between the maximum value of the underlying asset during the option's life and the initial asset value. Since the highest price of the asset during the option's life cannot be less than the initial price, this difference cannot be less than zero. It is shown that the value of this exotic timing option can be decomposed into two parts: a "lookback" put option and a forward contract on the underlying asset. The lookback option, which has a known solution, gives its holder the difference between