The computational hardness of pricing compound securities

Abstract

It is generally assumed that you can make a financial asset out of any underlying event or combination thereof, and then sell a security. We want to show that while this is theoretically true from the financial engineering perspective, compound securities might be intractable to price. Even given no information asymmetries, or adversarial sellers, it might be impossible or very computationally intensive to put a value on these, and the associated computational complexity might afford an advantage to the party with more compute power. We have proved a PSPACE complexity bound on pricing unbounded compound options without assuming information asymmetries, and have also obtained exponentially increasing lower bounds on the number of queries required to price k-layered securities.