Analytical pricing of single barrier options under local volatility models
研究了局部波动率模型下单一障碍期权的定价，通过对称化将下跌入局期权分解为三个标准欧式期权的组合，并用Aitken加速器近似定价，对其他单一障碍期权同样适用。
This paper considers a single barrier option under a local volatility model and shows that any down-and-in option can be priced by a combination of three standard European options whose volatility functions are connected through symmetrization. The symmetrized volatility function is approximated by a sequence of smooth functions that converges to the original one. An approximation formula is developed to price the standard European options with the approximated volatility functions. Finally, we apply the Aitken convergence accelerator to obtain an approximate price of the down-and-in option. Other single barrier options are priced in a similar fashion.