A tool that measures the changes in vega with respect to the passage of time. It is the second-order measure of derivative price sensitivity, expressed as the rate of change in vega (vega position) with respect to time. As time to maturity of a derivative (e.g., an option, a warrant, etc.) decreases, DvegaDtime is expressed as negative partial derivative:
Where: d1, d2 (see: Black-Scholes equation), T: time to maturity (of an option), σ: volatility, r: the risk-free rate, and b: the dividend yield (on the underlying)
Practically, DvegaDtime is expressed as the sensitivity for a 1% change in volatility to a unit of time (one day), and hence it is to be divided by the number of days (calendar or trading days).
