Asymptotics for short maturity Asian options in jump-diffusion models with local volatility
研究了含局部波动率的跳扩散模型中短期亚式期权的渐近行为，推导了Merton跳扩散、双指数跳和方差伽马模型的显式一阶渐近公式，并提出了满足短期约束的解析近似，经蒙特卡洛验证与数值模拟吻合良好。
We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process. The analysis for out-of-the-money Asian options is extended to models with Lévy jumps, including the exponential Lévy model as a special case. Both fixed and floating strike Asian options are considered. Explicit results are obtained for the first-order asymptotics of the Asian options prices for a few popular models in the literature: the Merton jump-diffusion model, the double-exponential jump model, and the Variance Gamma model. We propose an analytical approximation for Asian option prices which satisfies the constraints from the short-maturity asymptotics, and test it against Monte Carlo simulations. The asymptotic results are in good agreement with numerical simulations for sufficiently small maturity.