Estimation of risk-neutral processes in single-factor jump-diffusion interest rate models

Abstract

The estimation of the market price of risk is an open question in the jump-diffusion term structure literature when a closed-form solution is not known. Furthermore, the estimation of the physical drift has a high risk of misspecification. In this paper, we obtain some results that relate the risk-neutral drift and the risk-neutral jump intensity of interest rates with the prices and yields of zero-coupon bonds. These results open a way to estimate the drift and jump intensity of the risk-neutral interest rates directly from data in the markets. These two functions are unobservable but their estimations provide an original procedure for solving the pricing problem. Moreover, this new approach avoids the estimation of the physical drift as well as the market prices of risk. An application to US Treasury Bill data is illustrated. JEL classification: G12, G17.

A new technique to estimate the risk-neutral processes in jump–diffusion commodity futures models

“…Analogous results, but for diffusion processes, are also shown in [8]. Parallel results for one-factor jump-diffusion interest rate models can be found in [9] and [10]. In order to implement Theorem 1 we rely on numerical differentiation.…”

The Role of the Risk-Neutral Jump Size Distribution in Single-Factor Interest Rate Models

“…However, this approach does not allow us to estimate the market prices of risk, which are necessary to price interest rate derivatives, but they are not observable. Recently, [10] proposed a new approach for estimating the risk-neutral drift and jump intensity directly from market data and, hence, the market prices of risk do not have to be estimated. They proved the following result.…”

“…Reference [10] assumed that the jump size distribution under Q was known and equal to the distribution under P; that is, = 1. In this paper, we take one step ahead and we propose the following result to estimate the risk-neutral jump size distribution directly from yield curve data.…”

“…We have to estimate the drift and the jump intensity of the riskneutral compensated interest rate stochastic process. As this process is not observable, we use (8) and (9) with numerical differentiation and the Nadaraya-Watson estimator with a Gaussian kernel in a similar way to that with Assumption A3; see [10] for more details.…”

“…Recently, in jump-diffusion models [10] proposed a procedure for estimating the risk-neutral drift and jump intensity of interest rates directly from data in the markets, and therefore, the market prices of risk did not have to be estimated for pricing. As usual in the term structure literature, they assumed that the jump size distribution did not change with the risk-neutral measure.…”