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Grayson · 2024年09月26日

calibration

NO.PZ2018123101000102

问题如下:

Fujioka tells Maalouf that she has been reading about the use of Monte Carlo forward- rate simulation for fixed income valuation. She asks Maalouf to further explain this approach to her. Maalouf replies, “The Monte Carlo approach is quite different from the binomial tree approach I’ve been describing to you. Some of these differences include:”

Difference 1: The Monte Carlo approach does not require calibration, whereas the binomial tree approach does.

Difference 2: The Monte Carlo approach is typically employed when cash flows are path dependent, whereas the binomial tree approach only allows one expected cash flow per node, regardless of the path of interest rates.

Difference 3: The Monte Carlo approach randomly simulates a fixed number of interest rate paths and values the security only across those paths, whereas the binomial tree approach values the security across all possible interest rate paths on the tree.

Of the three differences Maalouf describes between the binomial tree approach to fixed-income valuation and the Monte Carlo simulation approach, he is least likely correct regarding:

选项:

A.

Difference 3.

B.

Difference 2.

C.

Difference 1.

解释:

A Monte Carlo forward rate simulation randomly generates a large number of interest rate paths that will correctly value benchmark bonds only by chance. A fixed amount, known as a drift term, is added to every forward interest rate on every simulated path to calibrate the simulation so that the values estimated for benchmark bonds equal their market prices.

calibration这个是什么意思呀?

1 个答案
已采纳答案

品职答疑小助手雍 · 2024年09月27日

嗨,从没放弃的小努力你好:


简单理解Calibration的含义:将市场数据代入模型中的,反求出来某些需要的参数。

在二叉树模型中:

我们假设利率是有波动的,但是不管利率怎么波动、演变出来的路径,仍要使得现金流折现的现值等于现在的市场价格。所以输入变量是市场价格,输出变量是利率路径。

更准确的说,我们知道了市场上benchmark bond的价格,能通过Bootstrapping的方法,求出来benchmark spot rate,进而求出implied forward rate。在二叉树中,有UP和Down,无论波动率是多少,某个时间点上的各种利率情况的均值,是implied forward rate。所以的确是利用市场数据,反求出来模型数据。

蒙特卡洛模拟也是一样的。

虽然各个路径都是按某些概率演变出来的,但是最终所有的路径求出来的债券现值,要等于市场价格。或者说,即便有千万种路径,总的来看,仍要符合债券价格求出的implied forward rate。输入数据是市场价格,反求的是各个路径。

在考试中,如果要考推算利率二叉树,一般会让求某个节点的forward rate,利用模型关系,代入就好。

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