Gaussian Estimation of One-Factor Mean Reversion Processes

Table 6

Comparison of Durham and Gallant, and proposed methods.

Parameter(∗)	Real	Bias^(a)	Bias^(b)	Real	Bias^(a)	Bias^(b)
𝛼	0,5	0,048900	0,037700	0,5	0,059730	0,021400
𝜇	0,06	0,000610	0,000127	0,06	−0,000310	−0,000021
𝜎	0,15	0,000200	0,000032	0,22	0,000120	−0,000046
𝛼	0,5	0,043780	0,032400	0,4	0,045890	0,032200
𝜇	0,06	0,000050	0,000016	0,06	0,000770	0,000046
𝜎	0,03	0,000010	−0,000003	0,15	0,000080	−0,000025

The data are obtained with 512 simulations monthly series (𝑑𝑡 = 1/12) with 1000 observations each, and the parameters are listed as real.
(a)Results of the method proposed by Durham and Gallant.
(b)Results of the method proposed in this paper.
(∗)In Durham and Gallant [4]: 𝜇=𝜃₁, 𝛼=𝜃₂, and 𝜎=𝜃₃.