Back to Basics: Volatility and Option Valuation

Teri Geske
Senior Vice President, Product Development

BondEdge for Windows allows investment managers to evaluate the impact of a change in volatility rates for different market sectors across a diversified portfolio. Since volatility is a critical component of option valuation, we thought it would be appropriate to review why volatility estimates are important in fixed income portfolio analysis and how you can measure the sensitivity of your portfolios to a change in volatility.

First, a brief reminder of why volatility is so important. Option theory reveals that, all other things being equal, an increase in volatility causes the value of an option to increase. If I have an option to buy avocados for $2 each for the next 12 months, and the price of avocados has been unchanged at $1.50 for the past 20 years, my option is worthless. However, if avocado prices have ranged from $0.90 to $3.25 over the past few seasons, my option is quite valuable. In fixed income portfolio analysis, volatility affects the value of callable (and puttable) bonds, mortgage-backed securities subject to prepayments (the right to prepay a mortgage is an option), adjustable rate securities with embedded caps and any other securities whose cashflows are potentially sensitive to changes in the level of interest rates. Since most of these instruments represent a short position in the option (with the notable exception of bonds with put options), an increase in volatility would cause the price of the security to decline. Or, if we hold price constant we can see that an increase in volatility causes a decline in a security's option-adjusted spread (OAS).

Although everyone agrees that volatility is an important variable in option valuation, the proper technique to use when estimating volatility is a topic of debate. In general, volatility is measured using historical data, or is implied from observed market prices (or some combination of the two). In BondEdge, the default volatility parameters (expressed as annual percentages) are based on historical observations because total return managers typically focus on returns over a fairly long period of time, e.g. 3 to 6 months. Some market participants (such as traders) with a shorter time horizon prefer to use implied volatilities, and the Volatility Appraisal report allows the portfolio manager to evaluate the impact of using different volatility assumptions on the duration and convexity of a portfolio. In fact, volatility estimates are often the primary cause of variations when comparing effective duration, convexity and OAS values from different sources.

While we typically use the term "volatility" in its singular form, to be more precise we should use the plural "volatilities", because the level of volatility differs along the term structure. Short term interest rates are generally more volatile than long term rates, and the analytical models in BondEdge take this into account by using different volatility rates along the term structure. The Volatility Appraisal report (under Portfolio-Simulation) allows you to specify the long and short rate volatilities for different segments of the market. Holding price constant, the effective duration, convexity and OAS of each security and of the portfolio are re-computed using the revised volatility estimates. The volatility parameters may also be modified in both Parallel and Specified Scenario portfolio simulations, where BondEdge calculates the total return, effective duration, convexity and other characteristics for the selected portfolio using the new volatility inputs. These features offer a portfolio-level analysis to complement the Security Valuation tool which allows you to analyze changes in volatility estimates (and other model parameters) for a single security.

Another way of measuring the impact of volatility on security valuation is described by the concept of Vega. Vega is defined as the price sensitivity to changes in volatility; securities (or portfolios) with a high degree of optionality have relatively high Vegas, whereas a security with no embedded options has a Vega of 0.00. Vega is one of the Risk Measures which may be computed in the Valuation screen or at the portfolio level using the Risk Measures report under the Simulation menu. We encourage you to use both Vega and the Volatility Appraisal and Simulations to understand how changes in volatility affect a diversified portfolio of securities with embedded options. As always, we welcome your feedback on this issue and invite you to suggest other topics for discussion.