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

Abstract

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 m + n model structure that bridges the gap in the literature by successfully pricing both interest rates and interest rate options. The first m factors capture the yield curve variation, whereas the latter n 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 m yield curve factors from the LIBOR and swap rates in the first step and the n 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%.

Market Expectations of the Short Rate and the Term Structure of Interest Rates: A New Perspective from the Classic Model

“…The average MAE (mean absolute error) across maturities is only 4.2bp, and the average VR (variance ratio) across maturities is as high as 99.9%. This is consistent with the previous literature on the fitting performance of 3-factor Gaussian dynamic term structure models, e.g., Heidari and Wu (2009). This table reports the summary statistics (sample mean, median, standard deviation, mean absolute error, maximum, and minimum) of the pricing errors over the daily sample from October 1994 to December 2009.…”

Forward-Looking Estimates of Interest-Rate Distributions

“…Allowing for these additional factors, the models are able to fit both interest rates and derivatives prices well. Heidari and Wu (2009) and Cieslak and Povala (2016) consider affine term structure models with conditional mean and volatility factors-Cieslak and Povala also use high-frequency data to obtain precise estimates of the physical second moments of yields. Filipović, Larsson, and Trolle (forthcoming) propose a model in which the state price density is a linear function of a state vector and show that it implies that bond yields are ratios of linear functions of those factors.…”

Predicting Interest Rate Volatility Using Information on the Yield Curve

“…Another weakness is the lack of unspanned volatility factors that are irrelevant to the cross‐section of yields. The necessity of such factors for describing joint data on bonds and options is emphasized by many studies (see, e.g., Collin‐Dufresne and Goldstein ; Heidari and Wu , ; Li and Zhao ; Han ; Jarrow et al. ).…”