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[The following information applies to item (i) only]. There are two bonds available in the...

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Finance

[The following information applies to item (i) only]. There are two bonds available in the market, Bond A and Bond B. Each of these bonds has face value $1mln, and they both mature on date T. The distribution of payoffs of the two bonds is given by:

Each bond has a probability of default equal to 3%

In the event of default, the bondholders lose 50% of the principal, but are able to recover 50%

If there is no default, a bond repays its principal, plus 3% interest, at maturity

There is no event in which both bonds default (that is, if one bond defaults, the other does not).

(i) Compute the 5% VaR measure for each of the following:

A portfolio that contains Bond A only;

A portfolio that contains Bond B only;

A portfolio that contains Bond A and Bond B.

Is the Value-at-Risk measure sub-additive in this case? Explain.

(ii) According to what we saw in the course, what is the purpose of volatility modelling? What feature of the data do volatility models attempt to reflect, and how can they be useful for risk measurement and management?

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