RM 432: Risk Management for Financial Managers

Assignment 2 April 2, 2021

1.中性风险概率与实际概率之间有什么区别？
2.使用Merton模型估算未来三年债务违约的可能性。

1个

0.1 8％3％

0.2 18％10％

0.3 40％20％

0.4 50％32％

0.5 5％65％48％

0.6的78％65％

0.7的90％80％

0.8的95％90％

0.9的98％95％

（a）库存X和Y的危险率。 （b）E {X}和E {Y}

（a）P {X≤0.6，Y≤0.9}
（b）P {X≤0.8，0.3≤Y≤0.6}

（c）E {X | Y = 0.7}（d）E {Y | X = 0.5}

（a）校长900
（b）当前值-90

2. 2年股票期权

（a）校长600
（b）当前值55

3. 7年期利率掉期。

2个

（a）校长600
（b）现值90

The assignment questions are to be completed in groups of two. Do not share your work with students from other groups. Only original work done by your group members is to be submitted. Plagiarism will not be tolerated in this class. The assignment will be marked based on (1) How you arrive at the solution, (2) Is the solution logical, consistent with the materials taught in class? (3) The presentation of your results. Remember, you must present your work in a clear and concise manner. How you communicate your work visually and verbally matters. You are require to submit a spreadsheet with your calculations for the numerical questions and a separate document with the answer for the conceptual questions and where you show the key steps involved to get the solution of the numerical questions.

Assignment due: April 10th by 11:59 pm (EST).

Question 1 (10 points)

The value of a company’s equity is \$2.5 million and the volatility of the equity is 50%. The debt that will have to be paid in three years is \$10 million. The risk-free interest rate is 2.5% per annum.

1. What is the difference between risk-neutral versus real-world probabilities?
2. Use Merton’s model to estimate the probability of a default on the debt in the next three years.

Question 2 (20 points)

Suppose that you observe the following empirical distributions for stocks X and Y .

1

Valuez P{Xz} P{Yz}

1. 0.1  8% 3%
2. 0.2  18% 10%
3. 0.3  40% 20%
4. 0.4  50% 32%
5. 0.5  65% 48%
6. 0.6  78% 65%
7. 0.7  90% 80%
8. 0.8  95% 90%
9. 0.9  98% 95%
1. Plot the probability density functions (pdf) for both stocks. (5 pts)
2. Compute (5 pts)

(a) The hazard rates of stocks X and Y . (b) E{X}andE{Y}

3. Assume that stocks X and Y have a correlation coefficient of 0.7. Use the gaussian copula to compute (10 pts)

(a) P{X 0.6,Y 0.9}
(b) P {X 0.8, 0.3 Y 0.6}

(c) E{X|Y =0.7} (d) E {Y |X = 0.5}

Question 3 (10 points)

Consider following transactions with the same counterparty 1. 3 year foreign exchange forward

(a) Principal 900
(b) Current Value -90

2. 2 year option on stock

(a) Principal 600
(b) Current Value 55

3. 7 year interest rate swap.

2

(a) Principal 600
(b) Current Value 90

Under Basel I, what is RWA WITH and WITHOUT netting if counterparty is a corporation? How much capital has to be set aside?