Managing Interest Rate Volatility Risk

Abstract

Interest rate contingent claims such as swaptions, caps and floors, callable bonds, mortgage-backed securities and many balance sheet items are subject to vega risk. Vega risk is defined as the interest rate volatility risk of an interest rate contingent claim, the uncertain change in volatility affecting the embedded option value. Since these contingent claims9 values are affected by the interest rate volatilities and these volatilities are stochastic, any hedging strategies, or more generally risk management, of these interest rate contingent claims should take the vega risk into account. However, based on market conventions, the interest rate volatilities are represented by a set of approximately 120 implied volatilities of the at-the-money swaptions over a range of tenors and expiration dates, called the volatility surface. And this volatility surface is stochastic. Controlling for these vega risks poses a significant practical challenge to managing these large number of risk sources. Thus far, there is a lack of solutions. This article introduces the key rate vega measures to manage the vega risks. Furthermore, the article shows how the key rate vega measures can depict the option risks embedded in an interest rate contingent claim and how they can be used for hedging a mortgage interest-only strip using key rate vega measures and key rate duration measures together, as an illustration of broader applications of the key rate vega measures.