@article{Jacquier:2011:10.1080/1350486X.2011.591159,
author = {Jacquier, A and Forde, M},
doi = {10.1080/1350486X.2011.591159},
journal = {Applied Mathematical Finance},
title = {Small-time asymptotics for an uncorrelated local-stochastic volatility model},
url = {http://dx.doi.org/10.1080/1350486X.2011.591159},
year = {2011}
}

Download

TY  - JOUR
AB  - We refine the work of Henry-Labordere, Lewis and Paulot on the small-time behaviour of a local-stochastic volatility model with zero correlation at leading order. We do this using the Freidlin-Wentzell theory of large deviations for SDEs, and then converting to a di®erential geometry problem of computing the shortest geodesic from a point to a vertical line on a Riemmanian manifold, whose metric is induced by the inverse of the diffsion coefficient. The solution to this variable endpoint problem is obtained using a transversality condition, where the geodesic is perpendicular to the vertical line under the aforementioned metric. We then establish the corresponding small-time asymptotic behaviour for call options using Holder's inequality, and the implied volatility. We also derive a series expansion for the implied volatility in the small-maturity limit, in powers of the log-moneyness, and we show how to calibrate such a model to the observed implied volatility smile in the small-maturity limit.
AU  - Jacquier,A
AU  - Forde,M
DO  - 10.1080/1350486X.2011.591159
PY  - 2011///
TI  - Small-time asymptotics for an uncorrelated local-stochastic volatility model
T2  - Applied Mathematical Finance
UR  - http://dx.doi.org/10.1080/1350486X.2011.591159
UR  - http://www3.imperial.ac.uk/people/antoine.jacquier08
UR  - http://www.tandf.co.uk/journals/titles/1350486X.asp
ER  - 

Download