A Joint Framework for Consistently Pricing Interest Rates and Interest Rate Derivatives

Dynamic term structure models explain the yield curve variation well but perform poorly in pricing and hedging interest rate options. Most existing option pricing practices take the yield curve as given, thus having little to say about the fair valuation of the underlying interest rates. This paper proposes an <italic>m</italic> + <italic>n</italic> model structure that bridges the gap in the literature by successfully pricing both interest rates and interest rate options. The first <italic>m</italic> factors capture the yield curve variation, whereas the latter <italic>n</italic> factors capture the interest rate options movements that cannot be effectively identified from the yield curve. We propose a sequential estimation procedure that identifies the <italic>m</italic> yield curve factors from the LIBOR and swap rates in the first step and the <italic>n</italic> options factors from interest rate caps in the second step. The three yield curve factors explain over 99% of the variation in the yield curve but account for less than 50% of the implied volatility variation for the caps. Incorporating three additional options factors improves the explained variation in implied volatilities to over 99%.