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CC · 2023年08月09日

MCS 路径依赖

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.

老师,MCS解决路径依赖问题,这个路径依赖,不是指的是利率的路径依赖么?题目说是CF,您能给我讲下这个利率和CF在这里的关系么?

1 个答案

pzqa015 · 2023年08月09日

嗨,爱思考的PZer你好:


这里的路径依赖不是利率的路径依赖,而是现金流的路径依赖。

蒙特卡洛模拟通过随机发射产生随机的一组利率(interest rate path),估值的时候,每个时间点的现金流(比如MBS的还款额)是依据当期的利率确定的,所以说是CF的path dependent。

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