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Abstract:
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We investigate the notion of stochastic volatility in the time series of functions. We first define a general functional analogue of the familiar stochastic volatility models employed in univariate and multivariate time series. Next, we describe a reduction of the functional specification to a finite dimensional vector time series model suitable for inference. Afterwards, we describe how to perform Bayesian inference for the functional stochastic volatility model.
By accounting for stochastic volatility, the model is capable of representing functional data where the degree of variation changes randomly over time, and this benefit is of key interest in uncertainty quantification problems. An application to daily SPX option surfaces demonstrates how the functional stochastic volatility model can be used to improve the accuracy of quantile estimates. In particular, we show that, compared to a constant volatility model, the functional stochastic volatility model can get more accurate estimates of Value-at-Risk for option portfolios by accounting for the heteroscedasticity endemic to option surface data.
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