Threshold estimation of Markov models with jumps and interest rate modeling

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

“…In this case, we have to estimate the drift and the jump size of the risk-neutral interest rate stochastic process. This process is not observable, but we can use (8) and (9) with numerical differentiation and the Nadaraya-Watson estimator with a Gaussian kernel. First, we estimate the risk-neutral drift as in A2 and, then, we estimate the volatility and the jump intensity with the moment equations as in A1.…”

“…In this paper, we use the 3-month Treasury Bill rates because [8] showed that any instrument with maturity below three months should not be used when estimating jump-diffusion processes.…”

“…Furthermore, the functions of the models are usually chosen to obtain a closed-form solution for the pricing problem. As a result, [1,7,8] proposed nonparametric jump-diffusion models of the short rates that nest most jump-diffusion processes, but a closed-form solution to the pricing problem cannot be obtained. Nevertheless, there are a lot of efficient numerical methods to provide accurate approximated solutions to the pricing problem.…”

Spot volatility estimation using delta sequences

“…One way of estimating instantaneous volatility consists in assuming that the volatility process is a deterministic function of the observable state variable, and nonparametric techniques can be applied both in the absence (see Florens-Zmirou [19], Bandi and Phillips [6], Renò [47] and Hoffman [23]) and in the presence of jumps in X (see Johannes [30], Bandi and Nguyen [5], and Mancini and Renò [36]). Fully nonparametric methods when volatility is instead a càdlàg process have been studied by Malliavin and Mancino [33,34] and Kristensen [32] in the absence of jumps, and by Zu and Boswijk [53], Hoffmann, Munk and Schmidt-Hieber [22] and Ogawa and Sanfelici [42] in the absence of jumps but with noisy observations.…”

Local Linear Estimation of Recurrent Jump—Diffusion Models

“…In this article, we only discuss infinite jump activity case, in other words, the jumps parts in this article can be compensated. Mancini and Renò (2010) used threshold method to study the finite jump activity case.…”