Short Maturity Forward Start Asian Options in Local Volatility Models

Dan Pirjol, Jing Wang, Lingjiong Zhu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and at-the-money, considering both fixed strike and floating Asian options. The exponential decay of the price of an out-of-the-money forward start Asian option is handled using large deviations theory, and is controlled by a rate function which is given by a double-layer optimization problem. In the Black-Scholes model, the calculation of the rate function is simplified further to the solution of a non-linear equation. We obtain closed form for the rate function, as well as its asymptotic behavior when the strike is extremely large, small, or close to the initial price of the underlying asset.

Original languageEnglish
Pages (from-to)187-221
Number of pages35
JournalApplied Mathematical Finance
Volume26
Issue number3
DOIs
StatePublished - 2019

Keywords

  • Asian option
  • Finance
  • large deviations
  • local volatility model
  • short maturity asymptotics
  • variational problems

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