Abstract
We present a rigorous study of the short maturity asymptotics for Asian options with continuous- time averaging, under the assumption that the underlying asset follows a local volatility model. The asymptotics for out-of-the-money, in-the-money, and at-the-money cases are derived, considering both fixed strike and oating strike Asian options. The asymptotics for the out-of-the-money case involve a nontrivial variational problem which is solved completely. We present an analytical ap- proximation for Asian options prices and demonstrate good numerical agreement of the asymptotic results with the results of Monte Carlo simulations and benchmark test cases in the Black{Scholes model for option parameters relevant in practical applications.
Original language | English |
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Pages (from-to) | 947-992 |
Number of pages | 46 |
Journal | SIAM Journal on Financial Mathematics |
Volume | 7 |
Issue number | 1 |
DOIs | |
State | Published - 2016 |
Keywords
- Asian options
- Large deviations
- Local volatility
- Short maturity
- Variational problem