Displaying similar documents to “Densities on locally compact abelian groups”

The d X ( t ) = X b ( X ) d t + X σ ( X ) d W equation and financial mathematics. II

Josef Štěpán, Petr Dostál (2003)

Kybernetika

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This paper continues the research started in [J. Štěpán and P. Dostál: The d X ( t ) = X b ( X ) d t + X σ ( X ) d W equation and financial mathematics I. Kybernetika 39 (2003)]. Considering a stock price X ( t ) born by the above semilinear SDE with σ ( x , t ) = σ ˜ ( x ( t ) ) , we suggest two methods how to compute the price of a general option g ( X ( T ) ) . The first, a more universal one, is based on a Monte Carlo procedure while the second one provides explicit formulas. We in this case need an information on the two dimensional distributions of ℒ ( Y ( s ) , τ ( s ) ) for s ≥ 0 , where Y ...

Modelling stock returns with AR-GARCH processes.

Elzbieta Ferenstein, Miroslaw Gasowski (2004)

SORT

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Financial returns are often modelled as autoregressive time series with random disturbances having conditional heteroscedastic variances, especially with GARCH type processes. GARCH processes have been intensely studied in financial and econometric literature as risk models of many financial time series. Analyzing two data sets of stock prices we try to fit AR(1) processes with GARCH or EGARCH errors to the log returns. Moreover, hyperbolic or generalized error distributions occur to...