Abstract
Chapter 2 introduced parimutuel pricing in its most basic form, a framework in which customers can only trade single state claims (no trading of vanilla options) and customers can only submit market orders (no submitting of limit orders). In this framework, pricing was based on two mathematical principles — the principle of “no-arbitrage” and the principle of “self-hedging.” Although this framework is widely used for wagering, it is not flexible enough to be useful for trading derivatives.
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Notes
The first state claim is the digital put struck at k and the Sth state claim is the digital call struck at K, both of which are tradable by customers in a parimutuel derivatives auction. If adjacent auction strikes are one tick apart, then the 2nd, 3rd, …, S — 1st state claims are digital ranges that customers can trade in a parimutuel derivatives auction. However, if all adjacent strikes are more than one tick apart, then customers cannot trade the 2nd, 3rd, …, S — 1st state claims in the auction. In fact, when strikes are more than one tick apart, derivatives can be replicated using a much smaller set of fundamental building blocks. Longitude’s parimutuel matching engine uses such an approach, and that approach is described in Lange, Baron, Walden, and Harte (2003, Chapter 11). This replication approach is related to the “supershare approach,” which was introduced by Hakansson (1976, 1978) and discussed in Cox and Rubinstein (1985).
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© 2007 Ken Baron and Jeffrey Lange
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Baron, K., Lange, J. (2007). Derivative Strategies and Customer Orders. In: Parimutuel Applications in Finance. Finance and Capital Markets Series. Palgrave Macmillan, London. https://doi.org/10.1057/9780230627505_5
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DOI: https://doi.org/10.1057/9780230627505_5
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-52000-8
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