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 = R_{1} x Digital Put Vega(K_{1}) + R_{2} x Digital Put Vega(K_{2})

+ R_{3} x Digital Put Vega(K_{3}) + R_{4} x Digital Put Vega(K_{4})

where the right hand terms are the digital put vega with strikes K_{1} < K_{2} < K_{3} < K_{4} respectively.

In this instance:

R_{1} = 40%, R_{2} = 30%, R_{3} = 20% and R_{4} = 10%

so that:

R_{1} + R_{2} + R_{3} + R_{4} = 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.