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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 pay a ...


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 ...


2

When building a SwaptionHelper, you have to tell QuantLib what kind of volatility you are inputting. There are three options: Black Vol, Shifted Black Vol and Normal Vol. Since you don't have black vol for most of the swaption surface (EUR) because of the negative forwards, you can either use shifted Black Vol or Normal Vol. In the example you are using ...


1

You may find this text helpful: Modern SABR Analytics : Formulas and Insights for Quants, Former Physicists and Mathematicians by Alexandre Antonov, Michael Konikov, Michael Spector. Focusing on recent advances in option pricing under the SABR model, this book shows how to price options under this model in an arbitrage-free, theoretically consistent ...


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 ...


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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