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1 – 6 of 6Diep Duong and Norman R. Swanson
The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of…
Abstract
The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of volatility, both discrete and continuous, and then we summarize some selected empirical findings from the literature. In particular, in the first sections of this chapter, we discuss important developments in volatility models, with focus on time-varying and stochastic volatility as well as nonparametric volatility estimation. The models discussed share the common feature that volatilities are unobserved and belong to the class of missing variables. We then provide empirical evidence on “small” and “large” jumps from the perspective of their contribution to overall realized variation, using high-frequency price return data on 25 stocks in the DOW 30. Our “small” and “large” jump variations are constructed at three truncation levels, using extant methodology of Barndorff-Nielsen and Shephard (2006), Andersen, Bollerslev, and Diebold (2007), and Aït-Sahalia and Jacod (2009a, 2009b, 2009c). Evidence of jumps is found in around 22.8% of the days during the 1993–2000 period, much higher than the corresponding figure of 9.4% during the 2001–2008 period. Although the overall role of jumps is lessening, the role of large jumps has not decreased, and indeed, the relative role of large jumps, as a proportion of overall jumps, has actually increased in the 2000s.
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Empirical findings on interest rate dynamics imply that short rates show some long memories and non-Markovian. It is well-known that fractional Brownian motion (IBm) is a proper…
Abstract
Empirical findings on interest rate dynamics imply that short rates show some long memories and non-Markovian. It is well-known that fractional Brownian motion (IBm) is a proper candidate for modelling this empirical phenomena. IBm. however. is not a semimartingale process. For this reason. it is very hard to apply such processes for asset price modelling.
Without using Ito formula, we investigate the IBm interest rate theory‘ We obtain a pure discount bond price. and Greeks by using Malllavin calculus.
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Hani Abidi, Rim Amami, Roger Pettersson and Chiraz Trabelsi
The main motivation of this paper is to present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable…
Abstract
Purpose
The main motivation of this paper is to present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.
Design/methodology/approach
The authors establish a result concerning the L2-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation.
Findings
The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension.
Originality/value
In this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.
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The purpose of this paper is to study the problem of optimal Ramsey taxation in a finite-planning-horizon, representative-agent endogenous growth model including government…
Abstract
Purpose
The purpose of this paper is to study the problem of optimal Ramsey taxation in a finite-planning-horizon, representative-agent endogenous growth model including government expenditures as a productive input in capital formation and also with hidden actions.
Design/methodology/approach
Technically, Malliavin calculus and forward integrals are naturally introduced into the macroeconomic theory when economic agents are faced with different information structures arising from a non-Markovian environment.
Findings
The major result shows that the well-known Judd-Chamley Theorem holds almost surely if the depreciation rate is strictly positive, otherwise Judd-Chamley Theorem only holds for a knife-edge case or on a Lebesgue measure-zero set when the physical capital is completely sustainable.
Originality/value
The author believes that the approach developed as well as the major result established is new and relevant.
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A. Thavaneswaran, J. Singh and S.S. Appadoo
To study stochastic volatility in the pricing of options.
Abstract
Purpose
To study stochastic volatility in the pricing of options.
Design/methodology/approach
Random‐coefficient autoregressive and generalized autoregressive conditional heteroscedastic models are studied. The option‐pricing formula is viewed as a moment of a truncated normal distribution.
Findings
Kurtosis for RCA and for GARCH process is derived. Application of random coefficient GARCH kurtosis in analytical approximation of option pricing is discussed.
Originality/value
Findings are useful in financial modeling.
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This article discusses issues common to the pricing of both insurance and finance. These include increasing collaboration between insurance companies and banks, deregulation of…
Abstract
This article discusses issues common to the pricing of both insurance and finance. These include increasing collaboration between insurance companies and banks, deregulation of various insurance and finance markets, integrated risk management, and the emergence of financial engineering as a new profession. Rather than attempting to give an exhaustive exposition of the issues at hand, the author highlights developments that, from a methodological point of view, offer new insight into the comparison of pricing mechanisms between insurance and finance.