Hedging short-maturity Asian options in local volatility models
arXiv:1911.12944
The paper derives short‑maturity asymptotic formulas for Asian option prices and deltas in local volatility models using a Gaussian approximation and Malliavin calculus, and validates the results with numerical experiments.
Abstract
This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a Hölder continuous payoff function in a local volatility model. The main idea of this analysis is that the local volatility model can be approximated by a Gaussian process at short maturity. By combining this approximation argument with Malliavin calculus, we derive short-maturity asymptotics for Asian option prices and deltas, and express them in terms of the local volatility function and the initial stock price. In addition, we show that the convergence rate of the approximation is determined by the Hölder exponent of the payoff function. Numerical experiments on concrete examples validate the effectiveness of the proposed method.