TextView?type=daily_treasury_yield_curve&field_tdr_date_value=all
2. Interest Rate Data: Daily Treasury Par Yield Curve Rates
All interest rate models are special cases of the general form of the short-term rate:
??(?? ) = (?? + ???(??))?? + ?(?? , ?)??
where f and g are suitably chosen functions of the short-term rate and are the same for most models.
θ is the drift of the short-term rate, and ρ is the mean reversion term. The term σ is the local volatility
of the short-term rate, and Z is a normally distributed Wiener process that captures the randomness
of future changes in the short-term rate.
The Kalotay-Williams-Fabozzi model assumes that changes in the short-term rate can be modeled by
using the above equation and setting f(r) = ln (r) (where ln is the natural logarithm) and ρ = 0.
? ??(?) = ???? + ????
The explicit solution to ?? can be found through Ito's Lemma:
?[??+Δ?] = ?? ?(?? )Δ?+ ??√Δ?
where Z is a normally distributed random variable with mean = 0 and variance = 1
Estimate θ and σ using historical data. In the context of this model, θ is the expected logarithmic change
in yield and σ is expected standard deviation. Simulate 100 interest rate paths for the next month fo
the 3-year & 5-year treasury rates using the Kalotay-Williams-Fabozzi Model and display the simulated
paths for each maturity in a separate graph.
? = ? [?? [
??+Δ?
??
]]
DATA SET
https:
home.treasury.gov
esource-cente
data-chart-cente
interest-rates/TextView?type=daily_treasury_yield_curve&field_tdr_date_value=all