On the functional estimation of jump–diffusion models

Bandi, Federico M.; Nguyen, Truong Thao

doi:10.1016/s0304-4076(03)00110-6

Cited by 147 publications

(188 citation statements)

References 30 publications

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“…Bandi and Nguyen [1] and Johannes [14] showed how to estimate the functions of a jump-diffusion process by means of their moment equations for interest rate models. However, this approach does not allow us to estimate the market prices of risk, which are necessary to price commodity derivatives but not observable.…”

Section: Exact Results and Approximationsmentioning

confidence: 99%

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

Gómez-Valle

Habibilashkary

Martínez-Rodríguez

2017

Journal of Computational and Applied Mathematics

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In order to price commodity derivatives, it is necessary to estimate the market prices of risk as well as the functions of the stochastic processes of the factors in the model. However, the estimation of the market prices of risk is an open question in the jump-diffusion derivative literature when a closed-form solution is not known. In this paper, we propose a novel approach for estimating the functions of the risk-neutral processes directly from market data. Moreover, this new approach avoids the estimation of the physical drift as well as the market prices of risk in order to price commodity futures. More precisely, we obtain some results that relate the risk-neutral drifts, volatilities and parameters of the jump amplitude distributions with market data. Finally, we examine the accuracy of the proposed method with NYMEX (New York Mercantile Exchange) data and we show the benefits of using jump processes for modelling the commodity price dynamics in commodity futures models. JEL classification: G13, G17.

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Section: Exact Results and Approximationsmentioning

confidence: 99%

“…This theorem can be proved with the infinitesimal operator (see [18]), as in [22] and [3], for diffusion processes, and in [14] and [1], for jump-diffusion processes.…”

Section: Empirical Applicationmentioning

confidence: 97%

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

Gómez-Valle

Habibilashkary

Martínez-Rodríguez

2017

Journal of Computational and Applied Mathematics

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Spot volatility estimation using delta sequences

2015

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Abstract. We introduce a class of nonparametric spot volatility estimators based on delta sequences and conceived to include many of the existing estimators in the field as special cases. The full limit theory is first derived when unevenly sampled observations under infill asymptotics and fixed time-horizon are considered, and the state variable is assumed to follow a Brownian semimartingale.We then extend our class of estimators to include Poisson jumps or financial microstructure noise in the observed price process. As an application of our results, we relate the Fourier estimator to a specific delta sequence obtained with the Fejér function. The proposed estimators are applied to data from the S&P500 stock index futures market.

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“…The subscript t-indicates that a function is evaluated just before each time step. Total variance combines the contributions of diffusion and jumps together [59][60][61].…”

Section: Model-based Indicatorsmentioning

confidence: 99%

Remotely-Sensed Early Warning Signals of a Critical Transition in a Wetland Ecosystem

et al. 2017

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Abstract:The response of an ecosystem to external drivers may not always be gradual and reversible. Discontinuous and sometimes irreversible changes, called 'regime shifts' or 'critical transitions', can occur. The likelihood of such shifts is expected to increase for a variety of ecosystems, and it is difficult to predict how close an ecosystem is to a critical transition. Recent modelling studies identified indicators of impending regime shifts that can be used to provide early warning signals of a critical transition. The identification of such transitions crucially depends on the ability to monitor key ecosystem variables, and their success may be limited by lack of appropriate data. Moreover, empirical demonstrations of the actual functioning of these indicators in real-world ecosystems are rare. This paper presents the first study which uses remote sensing data to identify a critical transition in a wetland ecosystem. In this study, we argue that a time series of remote sensing data can help to characterize and determine the timing of a critical transition. This can enhance our abilities to detect and anticipate them. We explored the potentials of remotely sensed vegetation (NDVI), water (MNDWI), and vegetation-water (VWR) indices, obtained from time series of MODIS satellite images to characterize the stability of a wetland ecosystem, Dorge Sangi, near the lake Urmia, Iran, that experienced a regime shift recently. In addition, as a control case, we applied the same methods to another wetland ecosystem in Lake Arpi, Armenia which did not experience a regime shift. We propose a new composite index (MVWR) based on combining vegetation and water indices, which can improve the ability to anticipate a critical transition in a wetland ecosystem. Our results revealed that MVWR in combination with autocorrelation at-lag-1 could successfully provide early warning signals for a critical transition in a wetland ecosystem, and showed a significantly improved performance compared to either vegetation (NDVI) or water (MNDWI) indices alone.

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On the functional estimation of jump–diffusion models

Cited by 147 publications

References 30 publications

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

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

Spot volatility estimation using delta sequences

Remotely-Sensed Early Warning Signals of a Critical Transition in a Wetland Ecosystem

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