The following document proposes the HW1-BSFX model to simulate TRM considering the stochasticity of FX rates used in derivatives valuation. The HW1-BSFX model is constructed using the Black-Scholes FX model with spot rate TRM and domestic (COP) and foreign (USD) interest rates as the results of the one factor Hull-White estimates. The calibration of the model is done using historic data from Colombian and American swap derivatives markets and USDCOP exchange rate options. To conclude, a Monte Carlo simulation is used to generate values of TRM with the proposed HW1-BSFX model vs the Black-Scholes FX with constant interest rates, noticing great similarities between the results for both models.
