Eachway call vega describes the change in the fair value of an eachway call due to a change in implied volatility. This vega is the first derivative of the eachway call value with respect to a change in implied volatility and is depicted as:
Evaluating Eachway Call Vega
Eachway Call Vega = 0.4 x Digital Call Vega(K1) + 0.6 x Digital Call Vega(K2)
where the right hand terms are the digital call vega with strikes K1 and K2 respectively.
Vega Over Time
Eachway call fair value is displayed against time to expiry in Figure 1. It is the same profile as Figure 2a of Eachway Call and it is added to this page for reference.
Figure 2’s 0.1-day profile is just the 99.00 eachway call vega alongside the 101.00 eachway call vega. The vega of the lower strike call and the vega of the upper strike call have no material effect on each other.
In contrast the 25-day vega at 98.00 is 0.0193 falls in a smooth line to -0.0185 at 102.00
At 98.00 and 102.00, with 25 days to expiry, a given incremental change in volatility will have the largest effect on the eachway call value.
Between the strikes there is no discernible pattern as the change in volatility has no consistent effect on the vega. What one can say with conviction is that from an asset price below the lower strike to above the upper strike, assuming enough days to expiry, the vega will decrease.
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Eachway Call Vega and Volatility
Figure 3 provides eachway call vega over a range of implied volatilities. What this graph is showing is how, with 5 days to expiry, a change in volatility will effect the vega at each implied volatility.
When there are 5 days to expiry, assuming high enough volatility (+10%) yet again vega declines in a smooth manner as the asset price increases.
When the volatility is just 2% the vega reflects the individual vegas of the 99.00 call and the 101.00 call.
Summary
The level of oscillation of the vega means that a short or long vega position is a lottery.