Short Maturity Asian Options for the CEV Model

带局部波动率的跳扩散模型中短期限亚式期权的渐近分析

Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility

本文在带局部波动率的跳扩散模型中推导了固定与浮动行权价亚式期权在短期限下的一阶渐近公式，覆盖 Merton、双指数跳跃和 Variance Gamma 等模型，并提出与蒙特卡洛模拟吻合良好的解析近似方法。

Short Maturity Asian Options in Local Volatility Models

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 floating strike Asian options. The asymptotics for the out-of-the-money case involves a non-trivial variational problem which is solved completely. We present an analytical approximation for Asian options prices, and demonstrate good numerical agreement of the asymptotic results with …

Short Maturity Forward Start Asian Options in Local Volatility Models

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 sim…

短到期机制下局部-随机波动率模型的亚式期权

Asian options for local-stochastic volatility models in the short-maturity regime

本文利用大偏差理论推导局部-随机波动率模型下亚式期权在短到期时的价外与价平价渐近式，通过在价平点附近展开二维变分问题得到隐含波动率水平、偏斜和凸性的显式近似，并在SABR、Heston等模型中验证了其定价效果。

短期到期亚式期权的若干渐近性

Some asymptotics for short maturity Asian options

针对短到期低波动率下亚式期权定价方法效率低的问题，本文用大偏差理论分析含跳跃项的局部波动率模型下的短期亚式期权，推导不同价值状态期权的价格渐近性，给出平值期权价格渐近的上下界。

Sensitivities of Asian options in the Black-Scholes model

We propose analytical approximations for the sensitivities (Greeks) of the Asian options in the Black-Scholes model, following from a small maturity/volatility approximation for the option prices which has the exact short maturity limit, obtained using large deviations theory. Numerical tests demonstrate good agreement of the proposed approximation with alternative numerical simulation results for cases of practical interest. We also study the qualitative properties of Asian Greeks, including new results for Rho, the sensitivity with respect to changes in the risk-free rate, and Psi, the sensi…