If I understand correctly what you are after is the marginal volatility contribution of a single asset to the portfolio. This is given by $$\sigma(X_j;X) = \sigma(X_j)\ \rho(X_j, X)$$ See here for ...

Say that you did the calculations in the classic regression way. If you stick the returns of your 4 asset returns in a $(T\times 4)$ matrix $Y$, and your 3 factor returns in a $(T\times 3)$ matrix $X$,...

Bloomberg has a Default Risk model, which is similar to what you are querying. You can see a screenshot in this PDF. There you can also see the kind of variables they use. You can access it by typing ...

Your second version is correct. The market determines the price of these bonds, from which the curve is derived. Your first version has a tiny speck of truth, in the sense that the central bank (e.g. ...

My opinion is that using rolling correlations of returns which themselves are computed over rolling windows is not reliable. Taking rolling windows smothers information. Instead, I would specify a ...

@Paul, I think you are correct. Your expression relates Gamma and Volatility Risk, as volatility risk is the risk of mis-estimating the future realised volatility. My only comment relates to your ...

I think that you have to distinguish between a 'fiat' (modern) monetary system and a 'gold standard' one. But sustainability will always be ensured endogenously, one way or another. Fiat money is ...

Have you tried to simulate both processes together from US close -> JP close -> US close -> JP close and so on? Where the correlation is fixed, but the volatility of each step is proportional to the ...

Levy models do that to some degree. They have the iid look and feel of the standard Gaussian models, but allow for higher moments. You can check the papers of Dilip Madan on Variance Gamma as a ...

Are you talking about something like this? $$dx(t)=\ldots\ dt+[x(t)]^\gamma\ dW(t)$$ If $\gamma$ is zero then you've got BM, if it's one you get GBM, inbetween you have a 'mix'.

Have you looked at money market ETFs? Something like Pimco's MINT http://finance.yahoo.com/quote/MINT

I suspect that you are mixing correlation and cointegration. What you describe as the co-movement of prices sounds like cointegration.

Spx is perfect for that. But for regime switching you need samples that span many years.

You can check the Euler-based risk attribution/ risk allocation, for example here: http://arxiv.org/pdf/0708.2542.pdf

$\alpha$ units of cash and $\beta$ bonds? Presumably you mean 'value' rather than 'return', since the SDF is not a percentage return but a 'discount factor'.

This is formally correct. However, I am not sure if practically it really makes any difference as Tasche points out: https://workspace.imperial.ac.uk/mathfin/Public/Seminars%202013-2014/...

Proof in the paper by Feller: http://www.jstor.org/stable/1969318

A large part of this comes from the simple combination of: 1. A downward sloping volatility skew (which corresponds to a skewed risk neutral distribution) 2. Sticky strike behaviour The vol that you ...

I assume that with 'yield curve' you mean US Treasury curve. The very short end is determined by the Fed rate, therefore one uses flat forward interpolation between Fed meeting dates (which are every ...

I would say that one should differenciate between what the formula means, how the inputs are calculated, and how one would use it. What is means: As noob2 points out it makes sense for simple ...

Is the stock so easy to manipulate? How much does she need to spend to drive the price against her, far enough to pass the strike and make a profit? For a stock that is that thinly traded to be ...

If we compound semi-annually and we have half year to go, then the current forward price is $$F = S \left(1+\frac{r}{2}\right) = 125 \left(1+\frac{0.10}{2}\right)$$ Isn't it as simple as that?
A simple shifting trick is to put $r(t)-f$ instead of $r(t)$ under the square root in your expression. Then $f$ is the new, possibly negative, interest rate floor. If, for example, $f=-100bp$ then the ...