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Quantitative Finance · Glossário

O que é HJM drift condition?

Definition 8.2 Rates, Credit, XVA and Risk · Capítulo 8 — Forward-Rate and Market Models

The HJM drift condition is the restriction that absence of arbitrage imposes on the drift once the volatilities are chosen:

α(t,T)=σf(t,T)∫tTσf(t,u) du.\alpha(t,T) = \sigma_f(t,T)\int_t^T\sigma_f(t,u)\,du .

Exemplos

Example 8.4 (Hull–White is an HJM model)

Chapter 7’s model has σf(t,T)=σe−κ(T−t)\sigma_f(t,T) = \sigma e^{-\kappa(T-t)}: its drift is σ2e−κ(T−t)(1−e−κ(T−t))/κ\sigma^2e^{-\kappa(T-t)}(1-e^{-\kappa(T-t)})/\kappa, 4.1 basis points a year for the ten-year forward with σ=80\sigma = 80 basis points and κ=3%\kappa = 3\%. Volatilities of this exponential form are exactly those for which the forward curve is driven by a single Markov state; a general σf\sigma_f makes the short rate path-dependent and the model can only be simulated.

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