Specimen 2010 question 4 (v) and 5 (i)

[Edwin]

Hi all,

I would appreciate help with the following;-

Queston 4 (v);-

I don't understand the examiners' points below from the solution;-

It will likely be
best to develop a simulation model which separately models the two different
time series and then seeks to allow for auto-correlations between the two time
series.

While I am happy with this comment, I don't understand why the examiners speak about "AUTO" - correlation. Isn't it just correlation? How can you have auto-correlation between diff time series? Isn't Autocorrelation the
correlation of a signal with itself?

Please also confirm if my understanding is correct i.e that the examiners are referring to say modelling the spread using Cholesky and the added normality
assumption of the spread. Ofocurse if the above is correlation and not "auto"-correlation.

Question 5 (i);-

I assume the 20% chance of unexpected loss under underwriting risk is just a thumb suck and is unrelated to the mean loss and the maximum loss derived before i.e 77 million and 168 million. This is a reasonable estimate, however I have no clue how the examiners arrived at their 91 million pounds loss. Was it just a thumb suck or could it have been estimated using some figures. With the rest of the risks following it is clear whether the examiners are thumb sucking or estimating. Some help will be appreciated as always.

 

[Oxymoron]

Hi all,

I would appreciate help with the following;-

Queston 4 (v);-

I don't understand the examiners' points below from the solution;-

While I am happy with this comment, I don't understand why the examiners speak about "AUTO" - correlation. Isn't it just correlation? How can you have auto-correlation between diff time series? Isn't Autocorrelation the
correlation of a signal with itself?

They mean to use the vector auto regressive model.

Please also confirm if my understanding is correct i.e that the examiners are referring to say modelling the spread using Cholesky and the added normality
assumption of the spread. Ofocurse if the above is correlation and not "auto"-correlation.

Let's say you are fitting a VAR model for series A and series B. After estimating the parameters and the best fit you will be left with one residual time series each for series A and series B. These residuals series' are correlated.

If you intend to simulate the residual series, you will need to use a copula function to capture their correlation. For the copula, you will need the matrix a correlation matrix of the residuals which is positive and semi-definite - for which you might need the Cholskey decomposition.

Hope this helps.

 

[Aswan]

1. what they mean as auto-correlation, is serial correlation. How Xt depend of X(t-1) or Y(t-1)

2. 77mil is the expected loss, thus when the insurer do the price, it was expecting profit of 43 mil to cover expense, cost of capital, risk premium etc2.
Thus, if the actual profit fall from they would consider them as loss. The 91 is derived from 168-77 = 91.

I notice, there are a lot of mistake in the examiner report.