Abstract:
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This paper investigates the notion of stochastic volatility in the time series of functions. Using linear mixed models, a functional analogue for stochastic volatility can be built from first setting a time-invariant basis, and then modelling randomness through the vector time series of random coefficients, which follow the usual stochastic volatility model. An application on daily SPX option surfaces is used to demonstrate the value of this approach, as the empirical behavior of such data are well-characterized by such a model and the functional time series approach can naturally facilitate daily changes in observation locations. The resulting methodology provides a description of joint movements of option prices which accounts for heteroscedasticity, and hence provides a more realistic characterization of risk for option portfolios.
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