In quantitative finance, we often wish to model the behaviour of asset prices given by a noisy Ito semimartingale ; unfortunately, this model is too complex to identify from price data. In this paper, we therefore consider efficient prices given by a time-changed Levy process ; this model is both identifiable, and replicates salient features of price data . We give a new estimate of the rate process in this model, which governs its volatility. Our estimate obtains minimax convergence rates, and is unaffected by arbitrary jump activity. Furthermore, it remains valid for the volatility in the general semimartingale model , obtaining convergence rates as good as any previously implied in the literature.
In quantitative finance, we often model asset prices as a noisy Ito semimartingale . As this model is not identifiable, approximating by a time-changed Levy process can be useful for generative modelling . We give a new estimate of the normalised volatility or time change in this model, which obtains minimax convergence rates, and is unaffected by infinite-variation jumps. In the semimartingale model, our estimate remains accurate for the normalised volatility , obtaining convergence rates as good as any previously implied in the literature.
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wish to model the behaviour of asset prices given by
model asset prices as
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; unfortunately,
. As
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too complex to identify from price data. In this paper, we therefore consider efficient prices given
not identifiable, approximating
R
; this model is both identifiable, and replicates salient features of price data
can be useful for generative modelling
R
rate process
normalised volatility or time change
D
governs its volatility. Our estimate
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arbitrary jump activity. Furthermore, it remains valid for the volatility in the general semimartingale model
infinite-variation jumps. In the semimartingale model, our estimate remains accurate for the normalised volatility