TextView?type=daily_treasury_yield_curve&field_tdr_date_value=all2. Interest Rate Data: Daily Treasury Par Yield Curve RatesAll interest rate models are special cases of the general form of the...

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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 for 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/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_yield_curve&field_tdr_date_value=all