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seven-zhu · 2022年10月11日

如题

  1. FRM II
  2. Credit Risk Measurement And Management

NO.PZ2020033003000019

问题如下：

The following statements are about Merton model. Which one is correct?

选项：

A.

Merton model can be applied to value the firm with a variety of debts with different coupon rates and time-to-maturity.

B.

The Merton model assumes that firm value is lognormally distributed with a constant volatility.

C.The firm value is allowed to jump from one value to another in the Merton model.

D.

For high leverage firms, the Merton model predicts higher default probabilities and lower recovery rates, which is consistent with the reality.

解释：

B is correct.

考点：Assumptions and Drawbacks of Merton Model

解析：选项A。Metron model 假设的是简单的资本结构。The firm has only one debt which is a zero- coupon bond with a face value of F and maturity of T.

选项B 正确。

选项C The firm value is not allowed to jump from one value to another in the Merton model.

选项D For high leverage firms, the Merton model predicts low default probabilities and high recovery rates,和现实正好相反。

section9 强化班30页，the distribution of equity values is not constant(volatility smirk). the non-constant volatility of equity is a violation of the BSM model. 所以公司的value是follow lognormal with constant volatility,然后equity的value是 not constant? 我有点搞混了

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pzqa27 · 2022年10月12日

嗨，从没放弃的小努力你好：


这里您可以根据BSM类比着理解，BSM 模型是C=SNd1)-Ke-rtN(d2)

而莫顿模型是Stock=call=VN(d1)-Fe-rtN(d2)

因此这里的V公司价值相当于原来BSM中的stock（股价）。BSM假设是股票价格的波动率恒定不变，这里类似的可以写出V（公司价值）的波动率保持不变。

我们知道BSM模型算出的Call option价格是恒定的，但是现实不是，因为股价的波动率不是恒定的，有波动率微笑的特性。同理这里原文也是一样的“the distribution of equity values is not constant(volatility smirk). the non-constant volatility of equity is a violation of the BSM model. ”原文是想说虽然莫顿模型算出的Equity是恒定的，但是真实情况不是，因为Firm value 的波动率不是恒定的，有波动率微笑的特性，这也就违反了BSM模型的假设

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