Option and Greek Sensitivity in a Discrete Trading Environment

In the real world trading happens in discrete manner. There can be expected changers in the environment during the trading intervals. Some may be perceived or expected (trader has taken a position on an impending change) and other may be surprise events.
dV = dS * ∂V/∂S + dσ * ∂V/∂σ + dr * ∂V/∂r + dt * ∂V/∂t

The chain rule can be used to:

• Look into price sensitivity by taking into account expected other parameter variations
• Deduce if the option pricing formula works in the current market by looking into if the price variation is inline with the changers in parameters using the Greeks

This would be a better framework to holistically look into the decay or variation of the Greeks used for hedging. For discretely delta hedging a portfolio the chain rule should be used since may of the parameters change in the intervals between hedging.

dDelta = dS * ∂Delta/∂S + dσ * ∂Delta/∂σ + dr * ∂Delta/∂r + dt * ∂Delta/∂t

© Suminda Sirinath Salpitikorala Dharmasena