Reconsidering the continuous time limit of the GARCH(1, 1) process

By Valentina Corradi. 2000

115 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/15712eb1c2b57b9c9dd2cf4e7f63093b36ec709f

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Citations in the corpus

Option Valuation with Long-run and Short-run Volatility Components (2008, unknown): “Heston and Nandi (2000) demonstrate that the Heston (1993) model is the limit of the GARCH(1,1) model we use in this paper, but the interpretation of limit results is somewhat tenuous (see for example Corradi (2000)).”
APPROXIMATING GARCH‐JUMP MODELS, JUMP‐DIFFUSION PROCESSES, AND OPTION PRICING (2006, unknown): “In fact, a deterministic volatility jump-diffusion model can also be obtained in a way similar to Corradi (2000).”
Jump Starting GARCH: Pricing and Hedging Options With Jumps in Returns and Volatilities (2006, unknown): “When the jumps are suppressed, both in returns and volatilities, our model reduces to a GARCH model, and option prices are given by to Duan’s GARCH option model. Just as Duan’s model provides a discrete time filter for an array of continuous time stochastic volatility models, including Heston (1993)”
A Practical Guide to Forecasting Financial Market Volatility (2005, methodology): “The SV models and the ARCH models are closely related and many ARCH models have SV equivalence as continuous time diffusion limit (see Taylor, 1994; Duan, 1997; Corradi, 2000; Fleming and Kirby, 2003).”
GARCH Models (2010, unknown): “12.3 (Another limiting process for the GARCH(1, 1) (Corradi, 2000)) Instead of the rates of convergence (12.30) for the parameters of a GARCH(1, 1), consider lim τ→0 τ−1ωτ = ω, lim τ→0 τ−sατ = 0, ∀s 1, lim τ→0 τ−1(ατ + βτ − 1) = −δ. Give an example of the sequence (ωτ , ατ , βτ ) compatible with…”
Recent Advances in ARCH Modelling (2007, background): “(1996a) in order to capture long memory effect in volatility, allows a hyperbolic decay of the coefficients bj which are positive, summable, and satisfy the unit root condition (26).”
An empirical comparison of GARCH option pricing models (2006, background): “2Duan (1996, 1997), Corradi (2000) and Nelson (1990), provide details on the relationships between univariate GARCH models and bivariate stochastic volatility models.”
Term Structure Models and the Zero Bound: An Empirical Investigation of Japanese Yields (2012, unknown): “Corradi (2000) questions the often-cited weak convergence of GARCH models to a continuous-time stochastic volatility model, and Wang (2002) shows that the likelihood function of the former does not converge to that of the latter model, except when volatility is deterministic.”
GARCH modelling in continuous time for irregularly spaced time series data (2008, methodology): “The convergence of the discrete- to the continuous-time processes is shown to be in probability in the Skorokhod metric and is therefore stronger than the previously mentioned weak convergence results of Nelson and Corradi.”
Recovering the Probability Density Function of Asset Prices using Garch as Diffusion Approximations (2001, background): “See, however, Corradi 2000 for conditions under which the diffusion approximation property fails. a greater flexibility for the estimation of both the simulated objective PDF of the asset price and the risk-neutral option pricing function q yr ŽTyt .”
Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling (2012, unknown): “In the literature, the link between GARCH-like models and continuous time models is well established, see e.g. Nelson (1990); Duan (1997); Corradi (2000).”
Unit Root Tests under Time-Varying Variances (2005, methodology): “This pattern corresponds to the non-degenerate large sample limit of GARCH processes, see Corradi ( 2000 ).”