#
Calculating Vega in Your Head
30 Nov 2019

**TL;DR**

## Derivation

Black Scholes for a Call/Put option is

Itâ€™s easy to see

With ATMF strike, ,

Here comes the approximation part, for short expiries and a wide range of vols,

Itâ€™s easier to check this plot of against volatility for different expiries. Immediately we see that even in an extreme market with 100% vol, the approximation is largely correct for short expiries.

## Shortcut

Recall that we derived the approximation of ATM option price in Calculating Option Price in Your Head,

immediately you have vega

## In Practice

We notice that ATM volatility does not have a strong impact on ATM Vega, this is expecially true for short-dated options.

In Forex, vega are often quoted in asset bps for 1% vol move. Above approximation intepreted in such a style is

Junior traders often find the below table of approximated vega for standard expiries helpful.

Expiry | 1d | 1w | 2w | 1m | 2m | 3m | 6m | 9m | 1y |
---|---|---|---|---|---|---|---|---|---|

Vega (asset bps) | 2.09 | 5.52 | 7.81 | 11.63 | 16.31 | 20.03 | 28.17 | 34.57 | 39.89 |

## Exercise

Q: What is the vega amount for a 100 mio notional USDJPY 1m ATM option?

A: From above table we know the vega in asset bps is 11.63, thus total vega in USD is

The vega amount is 116.3 K USD.

Til next time,

Jianfeng
at 22:08