Deriving Three-Month Forward Rates from Hull–White Short-Rate Paths

Summary

The document asks how to derive a three-month forward rate from short-rate paths simulated under the one-factor Hull–White model, with monthly time steps. It proposes using the model’s zero-coupon bond formula to obtain discount factors over monthly intervals, converting those to one-month forward rates, and combining the rates across three months. It also suggests adding a spread to represent the difference between the simulated rate and three-month LIBOR.

The question assumes a single curve and concerns claims contingent on three-month LIBOR. It gives no answer or validation, so the proposed aggregation and spread treatment are not established as correct. The note highlights a practical modeling issue: a short-rate path, a bond price, and a tenor-specific forward rate are related but are not interchangeable without specifying the relevant dates, compounding, and curve assumptions.

Key ideas

• The question uses Hull–White simulated short rates to calculate zero-coupon bond prices.
• Monthly discount factors can be converted into interval forward rates under stated conventions.
• The proposed three-month rate combines monthly forwards and adds a spread.
• The document does not establish whether this method correctly models three-month LIBOR.

Tags

# how to get 3 month Forward rates from Hull white model simulation?


# how to get 3 month Forward rates from Hull white model simulation?












I implemented the Hull White one factor model in Monte Carlo simulation, and got the short rate on each node (time step =1month). my question is how to get the forward rate from the short rate? I am using the formula for zero coupon bond P(t,T)=A(t,T)*EXP(−B(t,T)*rt) (J.Hull's book), P(t,T) can be the discount factor between t and t+ 1month and then can be converted into a 1 month forward rate. To get a 3 month forward rate, I integrated those three 1month forward rate and then added a 1month-3month spread to obtain the simulated 3 month forward rate. can anyone advice if this approach is reasonable? The claims in contingent on 3month libor, for now I am just assume single curve. Thanks!

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