Eachway put vega describes the change in the fair value of an eachway put due to a change in implied volatility. The eachway put vega is the first derivative of the eachway put with respect to a change in implied volatility and is depicted as:
where V is vega, P is eachway put value and sigma is volatility.
Evaluating Eachway Put Vega
Eachway Put Vega = R1 x Digital Put Vega(K1) + R2 x Digital Put Vega(K2)
where the right hand terms are the digital put vega with strikes K1 and K2 respectively, K1 being the lower.
R1 + R2 = 1 and R1 <
Vega Over Time
Eachway put and vega are displayed against time to expiry in Figure 1a and 1b respectively.
The 10-day (blue) profile steadily falls from right to left as the strategy increasingly becomes in-the-money so that increase in volatility risks the price of Corn falling out-of-the-money. The 4-day profile shows the wavy nature of two adjacent digital put vega, while the 0.2 day profile clearly distinguishes between the two separate options.
| European Digitals | Eachway Put | Eachway Put Delta | Eachway Put Gamma | Eachway Put Theta |
Vega and Volatility
Figure 2a presents the vega over a range of implied volatilities with the higher implied volatility of 30% providing the same gradual slope as the 10-day profile of Fig.1..
As the implied volatility falls the absolute values of the vega increases until the midpoint between the strikes is flat at zero and the vegas of the lower and upper strike are independent of each other.