# Tag Info

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### What's the difference between PV01 and DV01 of a bond?

They are both price changes in response to a 1 bp change. DV01 is valid for a single bond. It is the price change in response to a 1 bp change in yield of this instrument. It arises from the ...
• 9,117
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### Shape and geometry of the yield curve

You can't make any concrete statements about the monotonicity, convexity or even sign of the yield curve. Yields are almost always positive, and in the past (2007 and earlier) you could find people ...
• 5,628
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### Black-Scholes under stochastic interest rates

We assume that the short interest rate $r_t$ follows the Hull-White model, that is, the short rate $r$ and the stock price $S$ satisfies a system of SDEs of the form \begin{align*} dr_t &= (\...
• 20.5k
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### Deriving Interest Rates

There are two parts to your question and I'd like to answer them separately. Curve Construction On a daily basis, you can observe prices on a large variety of instruments, whose prices are driven by ...
• 10.9k
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### Why using the swap curve as riskfree rate and no longer gov bonds?

I guess it depends on what they're referring to... The traditional swap curve (LIBOR-based) is certainly not risk free, as evidenced by the experience of the financial crisis and the resulting ...
• 10.9k
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### Does banks' profitability really suffer under low interest rates

A simple correlation/beta analysis of the Banks-relative-to-market versus interest rates or bond yields will tell you that the effect is real enough, whether in Europe, the US, or Japan... Likewise, a ...
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### What is the trickiest thing to get right in Rates Quant recently (2019)?

Of course making money is always the key issue. That (not completely facetious) comment aside: On the practical side, in many firms IT is struggling with being clear, transparent, and intuitive in ...
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### When Fed stops QE, Treasury Futures will go down in price, so... LEAP Puts are a good idea?

Not saying this trade won't work, but there's certainly no guarantee that it will... Given that QE will stop in October is well teleported at this point and has been expected since last year, you'd ...
• 10.9k

### Quantitative strategies in the Fixed Income space

Here are some general directions: Alternative Risk Premia The ARP, or "smart beta," space has gained a lot of tractions over the past few years. These are rule-based strategies that provide ...
• 10.9k
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### Dec 16: FED rate hike?

Fed funds futures settle into the average daily Fed Funds effective rates over the month. The December 2015 futures contract therefore covers the current Fed funds target rate (0-25bp) for 16 days, ...
• 10.9k
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### How do we determine the "correct measure"?

Recall that any traded asset divided by a numéraire is a martingale under the measure associated to that numéraire. For the 3 interest rates you mention, the natural measure (namely the one that makes ...
• 7,251

### How does one estimate the probability of the Fed increasing its benchmark rate based on Fed funds futures?

There is actually a lot of art involved. The most simplistic framework is as follows: The first step is to obtain a list of FOMC meeting dates. These are available currently for 2015 and 2016 here. ...
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### Why do we discount in ois and not treasuries

There are two parts to this question: 1) Is OIS a good risk-free proxy? and 2) Why is OIS used to discount cash flows of derivatives. First, overnight indexed swaps, in the US, are indexed to the Fed ...
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### Two papers - two different solutions of the Ornstein-Uhlenbeck process

Note that the Ito integral of a deterministic integrand $f: \mathbb{R}_+ \rightarrow \mathbb{R}$ is normally distributed \int_0^t f(u) \mathrm{d}W_u \sim \mathcal{N} \left( 0, \...
• 5,800
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### Bond ETF vs Bond Future for longer term holding

This is a surprisingly complicated question that encompasses many moving parts. Without knowing exactly what your objectives are, it's a bit difficult to offer concrete advice, so I'll provide some ...
• 10.9k
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### What's Risk-Neutral in an Interest Rate Model?

It is a very interesting question. There is a brief explanation in the book Martingale methods in financial modelling. Basically, it says that, the interest short rate $r_t$ can be modeled in any ...
• 20.5k

### What is a regime switch?

Regime switching is another way to describe structural changes in a data series. For example, an inflation timeseries may change states from ARMA to linear as the economy moves from a period of ...
• 939
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### Why does one-factor short-rate model tend to produce parallel shift of the yield curve?

This has already been explained at the start of Chapter 4 in Brigo's book. Basically, for any affine model of the short rate $r_t$, the zero-coupon bond price has the form \begin{align*} P(t, T) = A(t,...
• 20.5k
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### What is a regime switch?

The idea of regime switching in volatility is rooted in the observation that volatility is usually fairly consistent and "mild", and occasionally very high, say during a market crash. The concept goes ...
• 288
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### How is this probability (45%) of Fed raising rates 3 times in 2017 calculated from Fed Funds market?

Using the following data from 12/18/16: Jan 2017 Fed funds futures =9936, Jan 2018 Fed Funds futures =9877 implies that 99.36-98.77 = 59bp of hikes are built in for 2017. IF you assume the only two ...
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### Price of bond future, given a specific interest rate?

Treasury bond futures are surprisingly complicated - this is an attempt at a short explanation, it will obviously gloss over some details, but hopefully gives you a flavour of how they are priced. ...
• 5,628

### Arbitrage possible with negative rate of interest?

As a practical aside on a large scale, I have heard the rumours of European banks and even a consortium of banks considering plans to build an ultra secure deposit facility for cash, and also the ECBs ...
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### Difference between 5Y breakeven inflation and 5Y5Y inflation forward?

I downvoted because I think the FED is very detailed in their documentation. The definition of a forward is a very basic financial question that a bit of google search can answer and not a quant ...
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### Why can sometimes stock prices rise when interest rates rise?

In the chart below, I'm showing the rolling correlations between stock returns and bond returns. (The relationship would be flipped if you are studying stock returns vs interest rates). As you can ...
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### Which interest rate model for which product

The model of choice depends on the purpose of the exercise. In general there are two types of models: Equilibrium models: These are general used use for "fitting" the spot curve to the discount ...
• 301
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### How can an inverted yield curve in a liquid market exist?

There are many reasons why a yield curve can be inverted. A default-free yield curve reflects a combination of - market expectation of future short-term interest rates; bond risk premium: usually ...
• 10.9k
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### Speed of mean reversion of an interest rate model

Mean reversion speed $\kappa$ is better interpreted with the concept of half-life, which can be calculated from $\text{HL} = \ln(2) / \kappa$. For example, if the mean reversion coefficient is \$\kappa ...
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### What is a central bank's shadow rate

It looks like it's referring to Wu and Xia (2016) shadow rates. Some more media coverage is here. The core idea of a shadow rate goes back at least to Fischer Black. Black (1995) Fischer Black's ...
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### Why are interest supposed deterministic for equity?

@Jan Stuller already pointed to Rho, an option's sensitivity to changes in the risk-free rate. This number is indeed very low indicating that a non-flat term structure may not dramatically misprice ...
• 13.9k