  Executing even moderately large derivatives orders can be expensive and
risky; it's hard to balance the uncertainty of working an order over time
versus paying a liquidity premium for immediate execution. Here, we introduce
the Time Is Money model, which calculates the Equilibrium Trading Horizon over
which to execute an order within the adversarial forces of variance risk and
liquidity premium. We construct a hypothetical at-the-money option within
Arithmetic Brownian Motion and invert the Bachelier model to compute an
inflection point between implied variance and liquidity cost as governed by a
central limit order book, each in real time as they evolve. As a result, we
demonstrate a novel, continuous-time Arrival Price framework. Further, we argue
that traders should be indifferent to choosing between variance risk and
liquidity cost, unless they have a predetermined bias or an exogenous position
with a convex payoff. We, therefore, introduce half-life factor asymptotics to
the model based on a convexity factor and compare results to existing models.
We also describe a specialization of the model for trading a basket of
correlated instruments, as exemplified by a futures calendar spread. Finally,
we establish groundwork for microstructure optimizations as well as explore
short term drift and conditional expected slippage within the Equilibrium
Horizon framework.
