Imperial College London
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ProfessorJackJacquier

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8569a.jacquier Website

 
 
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Location

 

804Weeks BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@unpublished{Jacquier:2019:10.2139/ssrn.3434073,
author = {Jacquier, A and Torricelli, L},
doi = {10.2139/ssrn.3434073},
publisher = {Elsevier BV},
title = {Anomalous diffusions in option prices: connecting trade duration and the volatility term structure},
url = {http://dx.doi.org/10.2139/ssrn.3434073},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - UNPB
AB  - Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to different distribution spread rates compared to standard models. In financial modelling this has been used to accommodate for random trade duration in the tick-by-tick price process. We show here that anomalous diffusions are able to reproduce the market behaviour of the implied volatility more consistently than usual Lévy or stochastic volatility models. We focus on two distinct classes of underlying asset models, one with independent price innovations and waiting times, and one allowing dependence between these two components. These two models capture the well-known paradigm according to which shorter trade duration is associated with higher return impact of individual trades. We fully describe these processes in a semimartingale setting leading no-arbitrage pricing formulae, and study their statistical properties. We observe that skewness and kurtosis of the asset returns do not tend to zero as time goes by. We also characterize the large-maturity asymptotics of Call option prices, and find that the convergence rate is slower than in standard Lévy regimes, which in turn yields a declining implied volatility term structure and a slower decay of the skew.
AU  - Jacquier,A
AU  - Torricelli,L
DO  - 10.2139/ssrn.3434073
PB  - Elsevier BV
PY  - 2019///
TI  - Anomalous diffusions in option prices: connecting trade duration and the volatility term structure
UR  - http://dx.doi.org/10.2139/ssrn.3434073
UR  - https://arxiv.org/abs/1908.03007v3
UR  - https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3434073
UR  - http://hdl.handle.net/10044/1/89037
ER  -
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