Module Units

## Vega and Rho

Having understood Delta, Gamma, and Theta we are now all set to explore the last two Option Greeks: Vega and Rho.

### What is Vega?

Vega, is the rate of change of option premium with respect to change in volatility.

### What is volatility?

Volatility is not just the up and down movement of markets. Volatility is a measure of risk and is estimated by standard deviation. We can estimate the range of the stock price given its volatility. Larger the range of a stock, higher is its volatility or risk. It’s the degree of uncertainty attached to a stock price.

Imagine a stock is trading at ₹100, with increase in volatility, the stock can start moving anywhere between 90 and 110. So, when the stock hits 90, all PUT option writers start sweating as the Put options now stand a good chance of expiring in the money. Similarly, when the stock hits 110, all CALL option writers would start panicking as all the Call options now stand a good chance of expiring in the money. Therefore, irrespective of Calls or Puts when volatility increases, the option premiums have a higher chance to expire in the money.

Example:

You want to Sell 500 CE options when the spot is trading at 475 and 10 days to expire.

Clearly there is no intrinsic value but there is some time value. Hence assume the option is trading at ₹20. You may write the options and pocket the premium of  ₹20/-

However, what if the volatility over the 10-day period is likely to increase – maybe election results or corporate results are scheduled at the same time. Will you still go ahead and write the option for ₹20? Maybe not, as you know with the increase in volatility, the option can easily expire ‘ITM’ hence you may lose all the premium money you have collected.

The option's Vega is a measure of the impact of changes in the underlying volatility on the option price. Specifically, the Vega of an option expresses the change in the price of the option for every 1% change in underlying volatility.

Options tend to be more expensive when volatility is higher.

Thus, whenever volatility goes up, the price of the option goes up and when volatility drops, the price of the option will also fall. Therefore, when calculating the new option price due to volatility changes, we add the Vega when volatility goes up but subtract it when the volatility falls.

### What is Rho?

Rho is the rate at which the price of a derivative changes relative to a change in the risk-free rate of interest. Rho measures the sensitivity of an option or options portfolio to a change in interest rate.

For example, if an option or options portfolio has a rho of 1, then for every percentage-point increase in interest rates, the value of the option increases 1%.

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Units 18/20