Option prices from operational-time reaction-boundary lattices
How market activity time, not clock time, shapes option prices
This paper shows that option prices depend on operational time — the actual pace of market events — rather than calendar time alone. The authors built a mathematical model showing how buy-sell activity at the bid-ask spread directly determines volatility and pricing, and how this framework explains why some market risks fall outside standard pricing models.
Financial traders and risk managers currently price options using models that assume steady time flow, but real markets operate in bursts — some moments see hundreds of trades, others see none. This work provides a concrete way to account for that variable rhythm, potentially improving how banks price derivatives and manage hedging when market activity is thin or uneven. It also clarifies which types of market risk standard models fail to capture, which matters for both regulators assessing systemic risk and traders avoiding blind spots.