Hot answers tagged valuation
13
The limitations of the Gaussian copula were well-known among the quantitative finance practitioners before the crisis. See this paper by D. Brigo.
To answer the question:
no "fat tails"
unable to fit the market prices without tweaks (base correlation) which make the model arbitrageable
it's a static model (e.g. forward-starting tranches are impossible to ...
9
If you want a 'pop science' account for it, the Wired article by Felix Salmon is a pretty good start.
If you want harder technical stuff, well then you can start at the Wikipedia article and its section on Applications and follow the references:
[...] Some believe the
methodology of applying the Gaussian
copula to credit derivatives to be one
of ...
7
Value has traditionally been one of the most important stock-selection signals for quantitative managers. However, since the late 2000s, following a rapid flow into quantitative investing, traditional value strategies have lost most of their predictive power and the returns generated from them have also become more volatile.
The typical approach of ...
6
There are "perpetual" bonds and preferred shares that are traded in the corporate credit markets that exactly match your conditions above. They are recorded in the 10-K at notional value $X$. The "close-out" feature is an embedded call.
You should assume your favorite stochastic interest rate (and/or credit) model and run a PDE solver, tree, or other grid ...
6
I can't speak for all structured products but valuing a MBS is straight-forward, but not easy. It's straight-forward because you just need to calculate the net present value of the discounted cash flows. That said, accurately determining those cash flows is hard.
The most difficult cash flows to determine--prepayments and defaults/severity--also have the ...
5
Most counterparty agreements specify some sort of ois rate for the interest paid/received on posted collateral. So the OIS rate is the appropriate one to use for discounting future cash flows.
Prior to 2008 the OIS/Libor spread was small and stable, so you didn't really need to worry about this, but now it's much larger, so people are taking it into ...
4
To create such a model, you'd start with some data, and then start fitting curves to it.
For example, let's take a company where there are reasonable consensus forecasts about the next few years' earnings; and let's assume you've got some time-series data on changes in those consensus forecasts, and changed in the price. You could then fit a model based on ...
4
I can offer you two explanations, one more economical, and the other mathematical.
The one based on economics is based on no arbitrage (and probably what you're looking for):
You are aware of the "Second" FTAP, which says roughly, that there is precisely one equivalent true/local/$\sigma$ martingale measure if and only if the market is complete, i.e. all ...
3
A paper by Gong, Smith, and Zou (2007) addresses your question exactly. From the abstract:
This paper explores the implications of hyperbolic discounting for asset
prices and rates of return. Hyperbolic discounting has no effect on the equity
premium. However, by making people less patient, causes stock prices to
be lower, and interest rates ...
3
I wouldn't put too much faith in IBES forecasts. You may remember this situation:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=889322
(In case the above link doesn't work, Google "Rewriting History Alexander Ljungqvist").
You'll find lots of excuses for worthless forecasts:
http://www.princeton.edu/~hhong/rje-analyst.pdf
Below is a graph that I ...
3
Take a look at Campbell's 2008 paper "Predicting Excess Stock Returns out of Sample". This paper is in response to Goyal & Welch's paper which argued that excess returns cannot be predicted out of sample. Also see Baekart and Ang's paper "Stock Return Predictability: Is it there?". A good theoretical framework that ties stock return predictability to ...
3
You should use the full yield curve, discounting cash flows at specific dates using the appropriate zero-coupon interest rate. As to which yield curve, that is often a matter of convention. Generally one uses the LIBOR/swaps curve for all but the most liquid products (in which case you use the treasury curve). The curve is constructed from LIBOR/Eurodollar ...
3
A condition for correct calibration of the short rate model is that it exactly reproduce the present values of fixed (option-free) cashflows - that is, that it give the same answer as ordinary discounting at the spot rate. If it doesn't, you've done something wrong - sort of like using a model that violates put-call parity. (Actually, it's exactly like ...
2
Mortgage backed securities are valued by calculating the net present value (NPV) of cash flows they are expected to generate. These cash flows are predicted using a model that incorporates all the contractual characteristics of the security and the underlying loans, as well as assumptions on things like prepayment speed, default speed, loss severity, and ...
2
The framework for valuing structured finance products in general is based on the nature of the cashflows in the product.
Decompose the constituent components of the structure.
Make some choices about handling the correlations between assets in the structure.
Review the covenants of the structure and their impact on the cashflows (sequence of events).
...
2
The OIS rate is more stable than Libor, right? And according to this article from Risk Magazine:
The party that is owed money at the end of the swap will have been paying an OIS rate on the collateral it has been holding, and so the ultimate value of the cash it will receive will be the sum it is owed minus the overnight interest rate it has had to pay ...
2
I think the formula you refer to is
$$ PV=\frac{C}{r-g} $$
If that's the case, then you do not subtract growth, the minus sign has an advantage on the present value.
The initial formula $PV=\frac{C}{r}$ assumes no evolution in $C$, but the other one assumes the that the payment will grow in time hence yes, you get paid for that.
1
Hyberbolic discounting seems to be operative in "bear" or panicked markets. That's when utilities, and other companies with heavily "front ended" earnings do relatively well, while cyclicals do poorly. People "know" that the cyclicals will (probably) do well some day, but they discount "delayed" earnings that will follow poor near term ones more heavily than ...
1
Alright, here's the proof (I think):
Statement of APT:
$$E(r_a)=r_f + \displaystyle\sum_{i=1}^n\lambda_i * cov(E(r_a), r_i)$$
Expand $E(r_a)$:
$$\frac{E(C_1)}{PV_0} - 1 =r_f + \displaystyle\sum_{i=1}^n\lambda_i * cov(\frac{E(C_1)}{PV_0} - 1, r_i)$$
Since $PV_0$ doesn't have any covariance with $r_i$, we can reduce the above to the following:
...
1
Nearly every options trader - and every options marketmaker - will hedge their derivatives exposure by trading the underlying.
So even if I buy a set of naked calls, my counterparty (e.g. whoever is writing me the options, usually a hedge fund or a bank) will have negative exposure to the stock and buy it to cancel out their risk.
Think of an option as ...
1
If you assume that you do not have any market risk (a strange assumption, but it would hold for example if you are fully hedged), then a (correctly) collaterlized derivative does not have any net future cash flow. Clearly: if the derivative contract has a cash flow of -X, its value will go down by X and the collateral account will have a cash flow of +X (the ...
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