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When trading American and Asian options in the FX derivatives market, banks must calculate prices using a complex mathematical model. It is often observed that different models produce varying prices for the same exotic option, which violates the non-arbitrage requirement of derivative risk management. To address this issue, we have studied a fully parameterized local volatility model for pricing American/Asian options. This model, when implemented using a grid or Monte-Carlo numerical method, can be efficiently and accurately calibrated to FX market skew volatilities. As a result, the model can provide reliable prices for exotic options during daily trading activities.