Greeks are trade or desk level first and second order sensitivities to changes in market rates. They are typically used in the front office for managing risk at the desk level. They provide a quick guide to traders as to the size and direction of risk and are often the subject of desk level limits.

At the trade level some Greeks can be calculated analytically (closed form) or numerically via stress testing. Vector Risk takes the latter approach and supports the Greeks listed below.

Theta

Traditionally theta is calculated on option products and is often described as "time value", where theta is the erosion of value in the option as time to expiry is reduced and the chance of the option ending up in-the-money is also reduced.

Another use of theta is portfolio decomposition. This calculation may be done for a longer interval (eg 1 month) and may involve a portfolio of cashflow products like IR swaps. It can be argued that "theta" in this case should be insulated from these cashflow events. The Vector Risk analytics calculate theta both ways; the simple way where the value date is moved and all else remains the same, and the cashlfow insulated approach where the "before" valuation excludes the maturing cashflows to align it with the "after" valuation, leaving only time value.

Vector Risk calculates both these values. "SimpleTheta" is the statistic which simply values the trade, and "Theta" is the statistic which excludes the maturing cashflows to leave the more traditional time value. The difference between these two values is the "Cashflow" effect in the P&L attribution analytic.


Delta

Delta measures the rate of change of the theoretical option value with respect to changes in the underlying asset's price.

A common way to calculate theta involves a small up shift and down shift of the price. If the prices emanating from these shifts are p_up and p_down then: delta = (p_up - p_down)/(2 * shift size)

Gamma

Gamma measures the rate of change of delta with respect to changes in the underlying price. It is a second order value that can be used along with delta to estimate the change in value due to larger shifts in price (at least for options with continuous payoff functions) by adjusting for convexity.

In line with the formula for delta above: gamma = (p_up + p_down - 2 * p) / (shift size ^ 2)

Vega

Vega measures the rate of change of the theoretical option value with respect to a 1% change in the implied volatility.

Rho

Delta measures the rate of change of the theoretical option value with respect to changes in the relevant risk free interest rate.