Hi,
the original text is sloppy. PD is here a random variable that can be 1 or 0. The probability of PD being one is p.
Expected value of PD:
E[PD] = p * 1 + (1-p) * 0 = p
Expected value of PD^2:
E[PD^2] = p * 1^2 + (1-p) * 0^2 = p
it follows that E[PD] = E[PD^2] = p
Which is a property of...
I’m not sure if this is still of interest, but the variance is not monotounius. That is also mentioned in Wikipedia:
https://en.m.wikipedia.org/wiki/Risk_measure#Variance
Davids intuition is correct.
Proof by counter example:
Assume X and Y are returns from two different Portfolios. Let X = c *...
1.+4. is answered by Nicoles links
2. no penalizing. You should guess in case you don‘t know the answer or your time runs out.
3. All questions have the same weight
I get to a different result.
The probability p of a specific bond to default is \[p=\frac{6}{68}\]
The losses are binominal distributed with standard derivation \[s=2 \cdot \sqrt{68 \cdot p \cdot (1-p)} = 4.68mn\]
Using the approximation as normal distribution, I get for the credit var:
\(CVaR...
For regulatory purposes you have to backtest on your actually portfolio. You have to show, that your modifications do not make a difference, which is probably not possible.
But that is just a problem for the start, right? In production you can backtest your model every day and store the result...
Hi delalma,
if I understand you correctly you need the backtest to validate your risk model and not for regulatory reporting, right?
I think the answer depends on the modifications that you make to get from inventory position to the risk position.
If these modifications are not part of your...
One possible explanation is a time lag between change in base rate and change in bond yield. Over what time interval do you calculate your changes? What base rates do you use?
1. Heteroscedasticity is not that bad. The least square estimator will not be the best estimator anymore, but it‘s still consistent and unbiased. So first order solution is to ignore the problem
2. There are Methods to deal with heteroscedasticity...
I just tried to calculate the risk neutral probabilities. If I‘m not mistaken, the parameters are not consistent.
The current spot rate is \(r_{0.5}=3\%\) for 0.5 years and \( r_{1} = 3.4\% \) at 1 year. That makes the forward rate \(r_{0.5, 1} = 3.77\% \). The problem now is, I think, that...
I think the bad reputation of Monotonicity is not justified. It is quite intuitive. In my opinion the confusion stems from the fact, that some text are vague in distinguishing future value and p/l.
The Dowd text that Davids cites is especially bad at that:
That is just not true. It is not about...
I thought this is easy to show, but then I found it surprisingly difficult.
Intuitive explanation:
The par rate is the rate of at which a swap has a value of zero. Each coupon payment is discounted with the spot rate of it‘s payment date. So the par rate is some kind of average of the spot...
I think, that is what I mean. I would calculate a tiny bit different:
3.112291/111.76394 = 2.7847%
and
2.9409852/102.94099 = 2.8570%
Even though the total sensitivity (absolute value) is higher for the 5% coupon bond (3.11 > 2.94), the percentage sensitivity is actually lower (2.78% < 2.86%).
Ah, great, now I understand your point better.
You equate sensitivity to changes in interest with duration (mod. duration vs. duration doesn‘t matter here).
The Sensitivity is the BPV in the above formula. As you can see, the Duration is the Sensitivity per NPV.
If you want you can say, that...
Hi akrushn2,
It does not.
Everything else equal a bond with a 2% coupon will have a greater duration than a bond with 5%.
I‘m not sure I get your whole point, but the duration is the weighted average over the cashflows. Lower coupons mean the principal payment in the end gets relative bigger...
Your parameters violate the assumption u > a.
Your jump up must be at least as big as the gain from the risk free rate.
That is because per definition the average gain of the asset under the risk neutral probabilities must equal the risk free rate. That is not possible if u is chosen too small.
Hi,
Assuming a continuous loss distribution f(x) with invertible cdf F(x):
\[ ES_{\alpha} =\frac{1}{1-\alpha} \int 1_{F(x)>\alpha} \cdot x \cdot f(x) \ dx \\ = \frac{1}{1-\alpha} \int 1_{p > \alpha} \cdot F^{-1}(p) \ dp \]
I personally find that the first integral is intuitively the definition...
I wonder if somebody could recommend a conference on financial risk management in the USA.
I’m trying to get an overview over current topics and challenges in the US and found the following major conferences:
1. Risk USA: http://www.riskusa.com/
2. Risk Americas...
A FXSwap can always be split into a FXSpot (the near leg) and a FXForward (the far leg). Both representations are equivalent in every way.
Of course that doesn’t mean that every pair of FXSpot and FXForward are equivalent to some FXSwap.
Also keep in mind, that a FXSpot and a FXForward are...
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