Passport Options: “Free Lunch” or a Unique Product?
Team Latte 15th March 2012
Passport Options are also known as “perfect trader” option and many financial journalists have called them “Free Lunch” options. A Passport Option is an option on the trading account. A trading account is the amount of money that an investor accumulates as a result of buying or selling a stock or a basket of stocks. At maturity, investment horizon, the investor walks away with all the money accumulated in this account or nothing, if, overall, there has been a loss. In other words, if the balance of the account is negative due to trading of stocks (assets), the investor simply walks away, whereas, if the balance is positive he walks away with the money. It is a call option on the profits made by the investors. Seems like free lunch? If it were, banks would not offer it to their clients. In 1997 Alex LiptonLifschitz, a quant working in Deutsche Bank together with his colleagues from Banker’s Trust, Tom Hyer and Dmitry Pugachevsky introduced the Passport Options in a paper titled “Passport to Success” in Risk magazine. Since then many banks in the Europe and Asia have tried to copy and modify this product and have offered it to high net worth individuals. Valuation of Passport Options can be done through techniques described in the branch of study known as Stochastic Control Theory.
Control theory, a branch of mathematics, is a theoretical description of how we can act optimally today to gain rewards in the future. This theory tells us how to optimizing a sequence of actions to attain some future goal or objective. It is used in the field of biology, biophysics, theoretical physics, engineering, financial economics and of course, quantitative finance. If the dynamics of the “control problem” is given by a stochastic differential equation, as is the case with many financial derivatives, then the field of study is known as Stochastic Control Theory. The most famous of such equations is the Stochastic Hamilton Jacobi Bellman (HJB) equation. Many engineers learn about Stochastic Control Theory via the topic of Dynamic Programming. JamilBaz and George Chacko, in their excellent book, Financial Derivatives: Pricing, Applicationsand Mathematics talk about this problem. Paul Wilmott in his book on Quantitative Finance talks about using Stochastic Control Theory to value Passport Option. Further, in 1999, in a follow through Paper titled “Similarities and SelfSimilarities” LiptonLischitz described techniques borrowed from physics to find out similarities between the pricing formulas for passport options, lookback options and Asian options.
The product has met with mixed success over the last decade. Many banks have sold this product, in its most vanilla form, to their high net worth clients in Asia but the product did not really take off. One reason could be that even within the quant desks of many banks the valuation of this product is not well understood.
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