利子の計算式の分類

最近ハル教授のオプション教科書の問題別冊の利率の微分方程式に関する問題を解こうとししています。　　分類項目は因子の数と均衡か無裁定の選択です。Examples of a one-factor model include: Ho-Lee, Vasicek, and Rendleman-Bartter. The move in the short rate is defined in terms of the current rate (the factor) and parameters (such as the long-term mean, drift, and volatility). For example, the Ho-Lee model is: dr = theta*dt + sigma*dz.
In these models, long and short-term interest rates move in parallel.
Examples of a two-factor model include: Longstaff and Schwartz, two-factor Heath, Jarrow, and Morton, and two-factor Cox, Ingersoll, and Ross (adaptation by other academics, the Chen model is a three-factor extension). The Longstaff and Schwartz model is: dQ/Q = (mu*X+theta*Y)dt+sigma*sqrt(Y)*dz. X is the economic factor affecting rates that is unrelated to production uncertainty, and Y is the factor that affects rates and production uncertainty. In these cases, the effect of the two factors does not necessarily induce a parallel shift in rates. The first factor causes similar responses from long and short-term rates. しかし第二因数が短期と長期の逆方向をさせる。For example, a rise in f2 may lead to a rise in the one-year rate and a fall in the twenty-year rate.
Equilibrium models do not necessarily correspond to the current term structure, and the term structure is an output of these models. Examples include the Vasicek and the Rendleman and Bartter models. No-arbitrage models take the term structure as input and are calibrated to the known short rates (drift term is time-dependent, allowing for such a compatibility, it seems). Examples include the Ho-Lee Model and the Heath, Jarrow, Morton Framework.
The bond prices derived from the interest rate processes result from solving the stochastic differential equation for dP. This equation apparently is derived from the properties of r, and r itself is the solution (in the Vasicek model) to the SDE dr = a(b-r)dt+sigma*dW.