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First, to make that clear: The Heston model does not generate negative volatility, but - for example - an Euler discretization of the Heston model may generate negative volatility (or variance). It is not a problem of the model. It is a problem of the numerical scheme. If you use an Euler scheme which generates negative volatility and then use any of the ...


4

It is not necessarily something that must be wrong with your model. Inherent in the Heston discretization methods of its continuous time dynamics is the possibility of negative values in the variance process. Here are couple solutions you can look at in order to "fix" your problem: Usage of different Euler schemes, such as the Full Truncation scheme. ...


4

For a US investor to hedge the bonds the investor would (1) Buy EURUSD in the Spot market, (2) Buy the German bonds with the EUR proceeds, (3) Short EURUSD in the forward market to provide a guaranteed repatriation rate when the bonds mature (thus avoiding FX risk). Currently the two year forward exchange premium/discount for the EURUSD is 532 forward ...


3

If you owe money to the bank, you will not receive a compensation. It might not exactly correspond to what you want, but here is my understanding. If we refer to the origin of the rates formation, you see two rates. e.g : https://www.ecb.europa.eu/mopo/implement/sf/html/index.en.html the marginal lending rate this one cannot be negative, ECB will not ...


2

Negative volatility means something some where along the lines something is inherently wrong with your model, double check your code and theory


2

Although Rf can be negative (but not too negative), Rm cannot be less than Rf as in your example. It is a non-equilibrium situation, no one would invest in risky securities if they have an expectation lower than risk-free securities. So Rm > Rf is a necessary assumption of the CAPM, whether rates are positive or negative. Also, algebra is algebra and the ...


2

There are by now a lot of papers on discretizations of Heston. One objective of them being to avoid negativity. As has already been said, the Heston SDE has no negative solutions, but a crude discretization does give negative variance with positive probability. If you want to do small steps, then using a log-normal approximation or the QE approximation ...


1

The capm doesn't care whether the risk free rate is positive or negative. In fact I'm not aware of any financial theory that is rendered invalid by negative rates. The only thing that's special about zero rate level is the fact that you can attain zero rate by holding physical cash. However it's impractical to hold large amounts of physical cash, so thats ...


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http://uk.reuters.com/article/2012/11/27/efsf-bond-idUKL5E8MR6I220121127 Nov 27: The order book on the European Financial Stability Facility one-year syndicated issue is over EUR 5bn according to a bookrunner on the deal. The eurozone rescue fund opened books this morning via JP Morgan, Morgan Stanley and Natixis at guidance of 0.23% to 0.25% with pricing ...


1

No. The shadow pricing of goods theory can explain the presently observed negative interest rates bonds. A shadow interest rate shows when the expected return is greater than interest rate (as firms wish to borrow more at given interest rate than they can) and opportunity cost of funds is greater than interest rate. Considering two additional ulimate local ...


1

1) JPY yield curve is currently upward sloping, not inverted... 2) Empirically, an upward sloping yield curve predicts recessions, not an inverted one. See this famous paper http://newyorkfed.org/research/current_issues/ci2-7.pdf


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