28
votes
Accepted
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 ...
- 9,402
25
votes
Accepted
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 ...
- 5,931
16
votes
Accepted
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 ...
- 5,101
15
votes
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 ...
- 491
13
votes
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 ...
- 11.8k
13
votes
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 ...
- 11.8k
12
votes
Accepted
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 ...
- 8,169
11
votes
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
\begin{equation}
\int_0^t f(u) \mathrm{d}W_u \sim \mathcal{N} \left( 0, \...
- 6,074
11
votes
Accepted
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 ...
- 11.8k
11
votes
Accepted
Volatility adjustment for SOFR/OIS caplet referencing LIBOR vol
I will refer to Risk-Free Rates (RFR) for greater generality, instead of OIS or SOFR. There are two dimensions to your question, I will treat them separately.
How to adjust a LIBOR vol surface to ...
- 8,169
10
votes
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 ...
- 979
10
votes
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.
...
- 5,931
10
votes
Accepted
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 ...
- 9,349
10
votes
Accepted
SOFR Discount Curve Construction in Nov 2021
Fixed vs SOFR swaps for longer maturities are very liquid, since the interbank market trades these directly now, and these are the best instruments to construct the long end of the curve (2yr to 50yr)....
- 17.5k
9
votes
Accepted
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,...
- 21.2k
9
votes
Accepted
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
9
votes
Accepted
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 ...
- 17.5k
9
votes
What's the difference between PV01 and DV01 of a bond?
Market practitioners many times refer to these two concepts in different ways and sometimes as the same thing. Not sure the different usages in regards to bonds, but here is my two cents, at least in ...
- 5,835
9
votes
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 ...
- 11.2k
9
votes
Hull-White model applied in practice
The Hull-White model is an no-arbitrage short rate model. It is used to price interest rate derivatives such as caps and floors. It generalises the seminal equilibrium model from Vasicek (1977).
The ...
- 16.2k
9
votes
Accepted
Caplet "in arrears" pricing formula
Let $P(t, T)$ be the price at time $t$ of a zero-coupon bond with maturity $T$ and unit face value. Consider the pricing of the caplet with payoff $(L(t_1; t_1, t_2)-K)^+$ at time $t_1$, where $0<...
- 21.2k
8
votes
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 ...
- 6,994
8
votes
Cap/Floor ATM Rate
The question is 1 year-old old but I will answer it anyway.
The ATM level (ATMF: at the money forward to be more precise) is the one giving you the same price for call and put, or in this case, the ...
- 2,230
8
votes
Accepted
Why are Interest Rate Swaps not valued using Monte Carlo Simulations?
Forward rates are determined from current spot rates bootstrapped from traded instruments. The reason is that if the forwards were different from the ones inferred from the spot rates, there would be ...
- 5,835
8
votes
Accepted
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 ...
- 16.2k
8
votes
Accepted
Dynamics of FX rate
I am answering now instead of commenting. The rate of change in FX is naturally forward looking in this case.
What you confuse is what happened to Spot due to changes in interest rate environments ...
- 9,349
8
votes
Pricing and hedging caps and floors on illiquid emerging markets
It could be worse. You're not asked to price rate exotics like accreters that might need more inputs besides implied vol cube :) and you're only asked to make markets. I.e., if I understand the ...
- 12.6k
7
votes
Accepted
SABR Calibration: Normal vs Log-Normal Market Data
I think you did something wrong in translating the input to numerics. As pointed out by dm63 normal vols are quoted in basis points.
Using equation A.67a) from the Hagan paper you linked we see (...
- 1,738
7
votes
Accepted
Black-Scholes vs Black equation
It's the forward rate which is fundamental to pricing for both stocks and interest rates. In the case of interest rates (unlike stocks) , it's difficult to compute the forward rate given the spot ...
- 17.5k
7
votes
Accepted
1y10y vs. 10y1y Swaption
Currently the USD 10Y swaprate is $2.93 \%$ and the ATMF 1Yx10Y implied volatility (relative) is $22.5 \%$ which corresponds to the Black model (absolute) volatility of about $4.15$ bp/day. The 1Y ...
- 3,700
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