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ACTSC445 Study Guide - Quiz Guide: Long-Term Capital Management, Space Shuttle Challenger, Emperor Xuan Of ChenExam


Department
Actuarial Science
Course Code
ACTSC445
Professor
Jiahua Chen
Study Guide
Quiz

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ACTSC 445/845 – Fall 2014
ASSIGNMENT 1 DUE: Friday 3rd October, 12.50pm
Hand in to Chen Xu in TA Office M3 3108 between 12.00pm and 12.50pm.
1. Investigate one of the following risk management failures. You should write a brief
summary of the case (aim for around 500 words), followed by a list of the most critical
risks, using the classification from the course notes. Explain briefly, for each risk, why
you consider it relevant to the case.
Select one from
The Walkerton Water Tragedy
The space shuttle ‘Challenger’
Long Term Capital Management
Notes:
- You may use any resources you find, but you should use your judgement as to the
reliability of your sources.
- You should cite your sources.
- You should write your answers in your own words unless you are directly quoting
from a source, in which case you should make it clear that you are quoting from
someone elses materials, and give proper attribution.
2. (a) Show that the CTE for N(µ, σ2) losses is
CT Eα=µ+σ
1αφQαµ
σ
where φ(z) is the standard N(0,1) density function, and Qαis the α-quantile of
the distribution.
(b) Hence, verify that the CTE is sub-additive for correlated normally distributed
losses.
3. A trader has a $0 VaR99% constraint for her 7-trading day losses. That is, her trading
strategy must have a 99% VaR less than or equal to 0 on a 7-day horizon. Assume 256
trading days in a year.
She has constructed a portfolio of derivatives on a stock with initial value S0= 100.
The value at T= 7/256 of ST/S0follows a lognormal distribution with parameters T µ
and T σ2, where µ= 0.05195 and σ= 0.31.
She has decided on the following strategy:
Purchase 1 million seven-day call options with a strike price of 87,
Sell short 1 million seven-day call options with a strike price of 88,
Finance the cost of the call options by selling short Mseven-day put options with
a strike price of 87.
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