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succi_z · 2023年05月19日

Difference 3

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,您好,这Difference 3描述的fixed number of paths指的是什么?fixed这种描述正确吗?

5 个答案

pzqa31 · 2023年05月23日

嗨,努力学习的PZer你好:


C是difference1

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努力的时光都是限量版,加油!

succi_z · 2023年05月23日

所以difference3不对 我们选C difference1?

pzqa31 · 2023年05月22日

嗨,从没放弃的小努力你好:


选一个最不对的,选C,difference3

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

succi_z · 2023年05月22日

C不是difference3?我们两看到的题目选项顺序不一样?

pzqa31 · 2023年05月21日

嗨,爱思考的PZer你好:


同学,关于difference3再补充一点,蒙特卡洛是随机模拟了利率路径,有可能都是利率上涨的路径,不包含下降的路径。而二叉树列出利率上涨下跌的所有路径,包含了所有可能的路径。严格意义上来说,这个difference3表述的不是很严谨。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

succi_z · 2023年05月22日

所以 题目问least likely,我们应该选difference 3?

pzqa31 · 2023年05月20日

嗨,努力学习的PZer你好:


difference1明显不对,二叉树和蒙特卡洛模拟都是需要calibration。difference3也不对。这道题答案有问题,何老师在经典题里提过,所以只能选一个明显不对的。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

pzqa31 · 2023年05月19日

嗨,爱思考的PZer你好:


不正确。蒙特卡洛模拟本身是一种统计方法,通过发射随机数模拟利率路径,比如发射一组随机数,就可以得到一条路径,我们可以把这个过程重复一千次,一万次,甚至更多,得到很多很多条路径,并不存在固定数量路径的说法。通过蒙特卡洛模拟可以得到任意想得到数量的路径,因为这只是一种纯统计学的方法。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

succi_z · 2023年05月20日

那么既然不正确,为什么不选A呢?

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