The Rho of an option measures the sensitivity of the option to the risk-free interest rate, r. The Vera of an option measures Rho's sensitivity to volatility, sigma. The following example illustrates the characteristics of the Vera of an option with respect to these two variables.
In this example, the Vera is defined as a function of the risk-free interest rate and volatility. To compute the Vera of a European call option with strike price 100 maturing in 1 year and with no dividends, we take:
This can be numerically solved for specific values of the risk-free rate, the dividend yield, and the volatility.
It is also possible to use the generic method in which the option is defined through its payoff function:
Here are similar examples for the European put option:
In this example, the Vera is defined as a function of the underlying asset price , and time to maturity, T. For a European call option, we will assume that the strike price is 100, volatility is 0.10, and the risk-free interest rate of 0.05. We also assume that this option does not pay any dividends.