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Pricing Options under Generalized GARCH and Stochastic Volatility Processes
Author(s) -
Ritchken Peter,
Trevor Rob
Publication year - 1999
Publication title -
the journal of finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 18.151
H-Index - 299
eISSN - 1540-6261
pISSN - 0022-1082
DOI - 10.1111/0022-1082.00109
Subject(s) - autoregressive conditional heteroskedasticity , bivariate analysis , volatility (finance) , econometrics , stochastic volatility , implied volatility , valuation of options , economics , volatility smile , limiting , mathematics , computer science , statistics , engineering , mechanical engineering
In this paper, we develop an efficient lattice algorithm to price European and American options under discrete time GARCH processes. We show that this algorithm is easily extended to price options under generalized GARCH processes, with many of the existing stochastic volatility bivariate diffusion models appearing as limiting cases. We establish one unifying algorithm that can price options under almost all existing GARCH specifications as well as under a large family of bivariate diffusions in which volatility follows its own, perhaps correlated, process.