TY - GEN

T1 - The computational hardness of pricing compound options

AU - Braverman, Mark

AU - Pasricha, Kanika

PY - 2014

Y1 - 2014

N2 - 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 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 computationally intractable to put a value on these, and the associated computational complexity might afford an advantage to the party with more compute power. We prove that the problem of pricing an option on a single security with unbounded compounding is PSPACE hard, even when the behavior of the underlying security is computationally tractable. We also show that in the oracle model, even when compounding is limited to at most k layers, the complexity of pricing securities grows exponentially in k.

AB - 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 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 computationally intractable to put a value on these, and the associated computational complexity might afford an advantage to the party with more compute power. We prove that the problem of pricing an option on a single security with unbounded compounding is PSPACE hard, even when the behavior of the underlying security is computationally tractable. We also show that in the oracle model, even when compounding is limited to at most k layers, the complexity of pricing securities grows exponentially in k.

KW - Computational complexity

KW - Computational finance

KW - Financial securities

KW - Pricing

UR - http://www.scopus.com/inward/record.url?scp=84893209354&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893209354&partnerID=8YFLogxK

U2 - 10.1145/2554797.2554809

DO - 10.1145/2554797.2554809

M3 - Conference contribution

AN - SCOPUS:84893209354

SN - 9781450322430

T3 - ITCS 2014 - Proceedings of the 2014 Conference on Innovations in Theoretical Computer Science

SP - 103

EP - 104

BT - ITCS 2014 - Proceedings of the 2014 Conference on Innovations in Theoretical Computer Science

PB - Association for Computing Machinery

T2 - 2014 5th Conference on Innovations in Theoretical Computer Science, ITCS 2014

Y2 - 12 January 2014 through 14 January 2014

ER -