As financial markets transition from IBOR to SOFR, new valuation methodologies are emerging to replace the ones used to model forward-looking rates. For banks and asset managers using tree valuation to price interest rate contracts, especially those with early termination right by either holder and/or issuer, the Willow Tree method can relieve some of the challenges presented by other models.
There has been a shift in how interest rate derivatives are valued, from term rates set at the start of a payment period to alternative risk-free rates (RFR) determined at the end of a payment period. RFRs are computed as an average of daily overnight rates over the accrual period. Because an RFR depends on daily SOFR up until the end of a payment period (thus it is path-dependent), its use creates challenges for lattice valuation models. By using the Forward Shooting Grid (FSG) method within the context of the Willow Tree model, the numerical method and analytic value converge when used to price both linear and non-linear payoffs referencing RFR.
Applying the Willow Tree model can be complex, so we have prepared a"Forward Shooting the Backward-Looking Rates" whitepaperto demonstrate how the model would work for SS&C Algorithmics RiskWatch clients. For simplicity in explaining the model, we ignore business conventions such as lookback or lockout to focus solely on the mathematical modeling aspect. We also assume that the payment period coincides with the accrual period, and use the terms interchangeably.