Eachway Put Vega

Eachway Put Vega iconEachway 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:

V = \frac{dP}{d\sigma}

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.

Eachway Put Vega w.r.t. Time to Expiry 100-50-0
Figure 1a – Eachway Put Vega w.r.t. Time to Expiry 100-50-0

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.

Eachway Put Vega w.r.t. Time to Expiry 100-25-0
Figure 1b – Eachway Put Vega w.r.t. Time to Expiry 100-25-0
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..

Eachway Put Vega w.r.t. Volatility 100-50-0
Figure 2a – Eachway Put Vega w.r.t. Volatility 100-50-0

 

achway Put Vega w.r.t. Volatility 100-25-0
Figure 2b – Eachway Put Vega w.r.t. Volatility 100-25-0

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.

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