Upcoming
This paper is in progress. The summary below previews what it will cover; the working paper and a less-technical write-up will be published here when ready.
Standard Geometric Brownian Motion is the workhorse of quantitative finance — but its assumptions about drift and volatility are routinely violated by real asset returns.
This paper develops a generalized GBM framework that relaxes the most restrictive constraints while preserving the analytical tractability that makes GBM so useful in the first place. Applications include derivative pricing and risk modeling for assets that don't behave the way textbook GBM says they should.