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Vega, Theta, and Rho

In our April and May articles, we saw how energy marketing organizations use Delta and Gamma to measure and manage the price risk in their energy portfolios. We learned that Delta is useful for managing positions with a linear sensitivity to price but is less effective when used to manage positions with a non-linear relationship to price (i.e. options). In last month’s article, we saw how Gamma can be used to supplement Delta as a measure of price risk for portfolios containing options. In this month’s article we’ll look at the other common measures of sensitivity used when managing options, including Vega (the portfolio’s sensitivity to changes in volatility), Theta (the portfolio’s sensitivity to changes in time, commonly referred to as time decay), and Rho (the portfolio’s sensitivity to changes in the risk free rate).

Option positions can be valued using a variety of methods, ranging from Black-Scholes and its variants (e.g. Black 76, etc.) to brute force evaluations (e.g. Monte Carlo, binomial/trinomial trees, etc.). The most popular method of valuing options positions is the Black-Scholes formula which utilizes a position’s underlying price volatility, interest rate, and time to expiry (along with the strike price and current market price) as inputs into its valuation logic. A discussion of Black-Scholes formula is beyond the scope of this article which will instead focus on explaining the purpose of the sensitivity measurements.

Determining the value of an option position is not as simple as determining the value of non-option positions. For example, the value of a fixed price position only requires knowledge of the fixed price and volume of the position along with the current market price. Similarly, the value of the option is dependent upon the strike price, volume and market price but its value is also dependent upon the amount of time left before the option expires, the volatility (or rate of change) of the market price, and other factors.

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