2014/06/23 by Henry Lam, Lam, Henry, Zhenming Liu +1
Computer Science · Economics, Econometrics and Finance · #Data Structures and Algorithms (cs.DS) #F.2 #FOS: Computer and information sciences #FOS: Economics and business #I.2.6 #Machine Learning (cs.LG) #Pricing of Securities (q-fin.PR) #cs.DS #cs.LG #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1406.6084
arxiv created 2014/06/23 · arxiv updated 2014/06/25
We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous structure as the Black-Scholes model, the widely popular option pricing model in stochastic finance, for both European and American options with convex payoffs. In the case of non-convex options, we construct approximate pricing algorithms, and demonstrate that their efficiency can be analyzed through the introduction of an artificial probability measure, in parallel to the so-called risk-neutral measure in the finance literature, even though our framework is completely adversarial. Continuous-time convergence results and extensions to incorporate price jumps are also presented.