Forward implied volatility expansion in time-dependent local volatility models******
We introduce an analytical approximation to efficiently price forward start options on equity in time-dependent local volatility models as the forward start date, the maturity or the volatility coefficient are small. We use a conditional expectation argument to represen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2014-09-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | http://dx.doi.org/10.1051/proc/201445009 |
| Summary: | We introduce an analytical approximation to efficiently price forward start options on
equity in time-dependent local volatility models as the forward start date, the maturity
or the volatility coefficient are small. We use a conditional expectation argument to
represent the price as an expectation of a Black-Scholes formula computed with a
stochastic implied volatility depending on the value of the equity at the forward date.
Then we perform a volatility expansion to derive an analytical approximation of the
forward implied volatility with a precise error estimate. We also illustrate the accuracy
of the formula with some numerical experiments. Some results and tools of this work were
presented at the conference SMAI 2013 in the mini-symposium ”Méthodes asymptotiques en
finance”. |
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| ISSN: | 2267-3059 |