Put accumulator vega describes the change in the fair value of a put accumulator due to a change in implied volatility. Put accumulator vega is the first derivative of the put accumulator with respect to a change in implied volatility. It is depicted as:
where P is the fair value of the put accumulator and σ is the standard deviation of returns of the underlying, or implied volatility in this context.
Evaluating Put Accumulator Vega
Put Accumulator Vega = R1 x Digital Put Vega(K1) + R2 x Digital Put Vega(K2)
+ R3 x Digital Put Vega(K3) + R4 x Digital Put Vega(K4)
where the right hand terms are the digital put vega with strikes K1 < K2 < K3 < K4 respectively.
In this instance:
R1 = 40%, R2 = 30%, R3 = 20% and R4 = 10%
so that:
R1 + R2 + R3 + R4 = 1
Put Accumulator Vega Over Time
With 2 days and over and asset price rising the vega has risen to be uniformly above zero. This is because the put accumulator is now out-of-the-money. A rise in volatility provides the trader a higher probability that the asset price will fall and the put accumulator be in-the-money.
Conversely, a fall in the asset price, say, down to 98.50 (the lowest strike) the trader now wants volatility to fall. The trader is in a winning position and a further rise in ‘vol’ increases the probability of the put ‘accy’ becoming out-of-the-money again.
| European Digitals | Put Accumulator | Put Accumulator Delta | Put Accumulator Gamma | Put Accumulator Theta |
Put Accumulator and Volatility
Figure 2 provides the put accumulator vega over a range of implied volatilities.
At the asset price of 98.20 the 4% volatility profile is roughly -0.0421. All of the profiles are negative at this asset level. It is stating that a rise in ‘vol’ will cause a negative price movement in the put accumulator. If the reader looks at Figure 2 of digital put vega the 5% profile is a great deal lower than the higher volatilities below the strike. When the option is in-the-money a rise in volatility threatens its winning status and the option value decreases.
When 18% vol is combined with a 25-day expiry and a structure of four separate digital puts the average price, the put accumulator, is not going to be a dramatic mover. The flat blue line makes that point.