## Vega and Rho- The Forgotten Greeks

Today, I was talking with one of my professors about how the different Greeks were mathematically derived (very stimulating conversation!), and I realized that I didn’t quite understand what Rho was. Or what Vega entirely was, for that matter.

So I did some research!

Vega is NOT implied volatility (which I thought it was). Vega is a MEASURE of volatility. IV is the expected volatility in the stock price, or how much it can move. Vega is the measure of the movement in the option price GIVEN a move in IV.

So a high vega means that the option is sensitive to changes in IV.

We find that vega is higher the farther out from the expiration date that we are. So an option with 45 days-to-expiration would have a higher vega than an option with only 5 days left to expiration.

Large vega also implies a large range of implied volatility. That makes sense, especially considering the fact that options far out in time have a higher vega value. The far out options can theoretically move between a larger range of prices than an option with only 5 days to expiration. It is much more probable that an option with 45 days left to expiration will move \$5 than an option with only 5 days left.

Vega also increases the closer we are to the stock price. So if we had a stock priced at \$30, the ATM strike (\$30) would be have a higher vega than the OTM strikes.

Therefore, the option with the LARGEST amount of vega overall would be the ATM strike far out in time. In our previous example, a 45 days-to-expiration \$30 strike with a \$30 stock price would have the highest amount of vega.

For example, let’s say our current stock price was \$130, and the price of the option was \$3, and option vega was 0.2. If we expect volatility to decrease from 20% to 10%, we would expect the option to decrease by [0.2 vega x (10 implied vol – 20 implied vol)] = -\$2

After the implied volatility decrease, the future expected value of the option is \$3 – \$2 = \$1

Rho is another Greek that no one ever really mentions. Rho is “a measure of the rate of change of the option price with respect to the interest rate.” There is a positive correlation between rho and option prices- the higher the rho, the higher the option prices. So we would see higher call prices with a 10% interest rate as compared to a 1% interest rate.

Luckily, Rho is one thing that we don’t really have to pay attention to, unless we are trading options on interest rate products. But, we should periodically check it, as a large and unexpected move in rho could majorly affect the prices of options.

Overall, vega and Rho matter, but it is better to invest your time in uncovering the intricacies of delta and theta. All the Greeks are important, but some are more important than others!

Disclaimer: These views are not investment advice, and should not be interpreted as such. These views are my own, and do not represent my employer. Trading has risk. Big risk. Make sure that you can balance your risk/reward, and trade small, and trade often.