Call accumulator vega describes the change in the fair value of a call accumulator due to a change in implied volatility. Call accumulator vega is the first derivative of the call accumulator with respect to a change in implied volatility. It is depicted as:
where P is the fair value of the call accumulator and σ is the standard deviation of returns of the underlying, or implied volatility in this context.
Evaluating Call Accumulator Vega
Call Accumulator Vega = Payout1 x Digital Call Option Vega(K1) + Payout2 x Digital Call Option Vega(K2)
+ Payout3 x Digital Call Option Vega(K3) + Payout4 x Digital Call Option Vega(K4)
where the right hand terms are the digital call vega with strikes K1, K2, K3 & K4 respectively.
In this instance Payout 1 = 10%, Payout 2 = 20%, Payout 3 = 30% and Payout 4 = 40% so that:
Payout 1 + Payout 2 + Payout 3 + Payout 4 = 1
Call Accumulator Vega Over Time
With 8 days and over the vega is always positive when the underlying is down at the lower strikes but turns negative as the underlying moves above the third strike. This is because at the higher underlying price the strategy is in a winning position. But the higher the ‘vol’ the greater the chance of the underlying returning to lower levels and lower payouts.
As time to expiry continues to fall the profile increasingly takes that of the individual digital call options theta profiles.
|European Digitals||Call Accumulator||Call Accumulator Delta||Call Accumulator Gamma||Call Accumulator Theta|
Call Accumulator Vega and Volatility
Figure 2 provides call accumulator vega over a range of implied volatilities.
Ultra low volatility provides yet again this manic swinging around as the strike in the immediate vicinity takes total control.
As ‘vol’ proceeds to rise from 1.5% the profiles soon follow the same smooth pattern which moves smoothly from positive to negative call accumulator vega.
If you took out the 0.1 & 0.5 day expiries from Figure 1 and took out the 1.50% volatility profile from Figure 2 the call accumulator vega is of value.