期权定价翻译

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在一篇期权定价文献中看到这句话，是外行人，想问下这一句要如何翻译呢？？
Approximating the early exercise surface

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关键词：期权定价 exercise Surface Approx Early exercise 外行人 如何

是接近提早行权临界值的意思吗？
能不能整段或整句帖出来？

陈振聪 发表于 2015-2-23 14:41
是接近提早行权临界值的意思吗？
能不能整段或整句帖出来？

11. Approximating the early exercise surface
The idea of approximating early exercise boundaries has gained popularity in pricing standard12 American options; Ju [22]uses multi-piece exponential functions to approximate the early exercise boundary of the American put option. Chiarella et al.[8] approximate the value function using Fourier–Hermite series expansions. Ait-Sahlia and Lai [3] approximate Kim’s (1990)early exercise boundary with a piecewise linear function. They first discretise the time domain into equally spaced sub-intervals.Linear interpolation is then incorporated to fit the early exercise boundary between two successive subintervals thereby generating the entire free-boundary. Mallier [28] consider series solutions for the location of the early exercise boundary closeto expiry.Approximation techniques have also been generalised to American options under stochastic volatility. Broadie et al. [6]have shown empirically in the single stochastic volatility case that ln bes; vT can well be approximated by a function that islinear in v. Based on these empirical findings, Tzavalis and Wang [35] have expanded the logarithm of the early exerciseboundary using Taylor series around the long-run volatility. This expansion yields two unknown functions of time which they later determine using Chebyshev polynomial expansion techniques. Instead of applying a Chebyshev approximation,Adolfsson et al. [2] use numerical integration techniques and root finding methods to find these unknown functions of time.This method proves to be adequate enough in terms of accuracy and computational speed as compared to other valuationmethods that they consider. It is this approach that we employ in this paper.

xiaobingsen 发表于 2015-2-23 16:14
11. Approximating the early exercise surface
The idea of approximating early exercise boundaries  ...

整篇就是这个标题有surface, 很难判断准确是什么意思
但根据这个文献综述，应该就是“提早行权的临界值的迫近（估算）方法”的意思了。
PS，我也是行外人

可能是stopping time的临界线