A new local volatility model called the collocating local volatility (CLV) framework has been developed to efficiently price exotic derivatives like callable basket options. Unlike other models, the CLV model can handle multiple dimensions easily and requires less computational time for calibration. This model is almost perfectly calibrated to implied volatility smiles/skews at specific expiries and allows for control of forward volatilities without affecting plain vanillas. It only takes a fraction of a second to calibrate to simple vanilla products.