Questions tagged [interest-rates]
An interest rate is the rate at which interest is paid by a borrower (debtor) for the use of money that they borrow from a lender (creditor).
995
questions
12
votes
2
answers
2k
views
Differences between main classes of interest pricing derivatives models
There seems to be 3 main classes of interest rate pricing models: 1) Short rate models, 2) Heath Jarrow models and 3) Libor Market Model. My book doesnt seem to explain why we need all these different ...
- 2,472
4
votes
0
answers
222
views
IR Cap Forward Premium
A well known broker quotes cap/floors as spot premium for ATM straddles but forward premium for the skew, given that the difference between spot premium and forward premium is that the option is not ...
- 575
1
vote
0
answers
140
views
Interest rate risk calculation for Banking book
There is a detailed discussions on the Interest rate risk for Banking book. For Floating rate bond, this states like below -
such positions generate cash flows that are not predictable past the
next ...
- 752
0
votes
0
answers
65
views
Is there no problem when par rate is used for IRS stress-test?
I want to do stress-test such as principle component analysis on IRS(interest rate swap) in order to calculate risk for the future change in interest rate. However it is so confusing which interest ...
- 1
2
votes
0
answers
139
views
Pricing kernel representation
I am reading this paper https://mpra.ub.uni-muenchen.de/4969/1/MPRA_paper_4969.pdf pp.6-7 on discrete-time bond pricing. The model adopted is a a common affine model,
the short rate follows
\begin{...
- 21
3
votes
2
answers
252
views
What is the Q-dynamics of affine bond prices when r is described by the given model?
Assuming an Affine term structure model, where bond prices arebe defined as: $$P(t,T)=\exp({A(t,T)-B(t,T)r_t)}$$ and describing the Q-dynamics of the short rate according to the model: $$dr_t=ar_tdt+\...
- 221
1
vote
0
answers
41
views
Interest rate model and premia with economical thinking
I heard the background about interest rate models from my coworker.
Especially it gives intuition to me that affine short rate model means it estimate long term interest rate by linearly add premia ...
- 303
0
votes
1
answer
116
views
Is the $NPV$ always a decreasing function in $r$
I was able to prove that, for positive Cash Flows $f_i$ and any value of $f_0$, the $NPV$ function is decreasing in $r$, hence, for $r_m<r_p=IRR$, then $NPV(r_m)>NPV(r_p)=0$.
$$
NPV(r,f_i)=\sum_{...
- 101
1
vote
2
answers
1k
views
Calibrate Hull-white one factor model with swaption in analytical formula
I've been trying to calibrate Hull-white one factor model with swaption but I have a trouble making closed form solution of swaption
Below is the part of paper I've been referencing to
https://people....
- 13
1
vote
1
answer
108
views
Implication of Humped Spot Curve on future spot curve(s)
I'm currently implementing a G++ model (Two Factor Hull & White model with constant parameters) on zero curve bootstrapped from USD IRS.
Currently, USD IRS is humped at 30 years; swap rate goes up ...
- 11
1
vote
1
answer
179
views
What is the correct volatility to use for inverting Black76?
I'm using VCUB on Bloomberg for ATM cap volatilities and have noticed there are a few "flavors" of volatilities. I would like simply use ATM flat vols to bootstrap forward volatilities from ...
- 11
0
votes
1
answer
298
views
Hedging with FX swaps
I am trying to get the mechanic of the swap rollover. Funds usually hedge FX risk of their long term foreign assets (eg UST) with short term FX swaps (usually maturity < 1yr), by rolling over fx ...
- 341
7
votes
4
answers
3k
views
Two practitioner questions about asset swap spreads
I have two questions regarding the terminology used on the practitioner side regarding asset swap spreads. Asset swaps are mainly used to retain the credit exposure of a bond while minimizing the ...
- 147
0
votes
0
answers
91
views
Where can (current) interest rate cap prices be found?
I'm somewhat new to interest rate models and am interested in obtaining ATM cap prices and volatilities for calibration purposes (Black-Derman-Toy, Hull-White, etc.). Ideally, this would enable me to ...
- 11
0
votes
2
answers
1k
views
How is calculated the futures/forward convexity adjustment for FX?
I could find lots of stuff online for IR derivatives but it seems there isn't too much on FX for this specific adjustment.
- 341
0
votes
1
answer
1k
views
FX swap implied yield from bloomberg
I am trying to reproduce the bid EUR implied yield I see in the screenshot below for 1y tenor which is -0.6226%.
EUR implied yield bid = spot_bid/fwd_bid *(1+i_USD_bid) - 1
Inputs from BBG terminal:
...
- 341
0
votes
0
answers
61
views
Euribor + margin
I have this bond assigment where I have to calculate the CF each quarter, given a constant EURIBOR3M rate of -0,539%. There is also a 1,6% margin per annum that I have to take into account. The ...
-3
votes
1
answer
54
views
Using compound interest rate in wrong way
I will explain the problem with an example.
Today (14/03/2021) y agree a Zero-Coupon Mortgage with a nominal of a milion dolars an with an annual interest rate compounded annualy and with an ACT/360 ...
- 179
3
votes
1
answer
189
views
Missing observations in ICE Swap rates
While searching time-series data for different interest rate benchmarks, I found that for the USD, all observations are missing for the period between March 2020/April 2020.
This discontinuity is ...
- 1,396
1
vote
1
answer
87
views
Why can a two-factor interest rate model not be used to value a coupon bearing bond as the sum of options on ZCBs
I am currently reading some notes which state that
For one-factor models, the value of a European option on a coupon bond can be calculated as the sum of European options on zero-coupon bonds (ZCBs). ...
- 439
2
votes
2
answers
568
views
FX Forwards collateral and discounting
What is the market convention for discounting the future cash flows of FX forwards? In particular, I would be interested to know what discounting curves are used for both collateralised and not ...
- 341
1
vote
1
answer
5k
views
resettable/MtM cross currency swaps
I am trying to understand the mechanics of resettable xccy basis swaps and put together a numerical example. I'd like to know if 1) periodic interest payments are calculated on the original notional ...
- 341
0
votes
1
answer
140
views
Can both good buying and good selling cause a bond to go special on repo?
A bond is known to go special when its repo rate gets particularly low relative to the GC (General Collateral) repo rate.
In my mind, this can be caused by two scenarios:
1. Institutional interest to ...
- 419
2
votes
1
answer
462
views
AUD funding rates
I am looking into into AUD rates and I am a little confused. I tried to summarise below my doubts.
FX swap basis (difference between AUD FX swap implied rate and AUD OIS rate). Before covid-19 it has ...
- 341
0
votes
1
answer
85
views
Fed fund market after QE
I read that before 2008, reserves of the banking system (vault cash and reserves at the Fed) fluctuated between \$40 billion and \$80 billion. However, as a result of quantitative easing, reserves ...
- 469
-3
votes
1
answer
169
views
Issue with Monte Carlo Simulation on an interest rate tree in Excel
I need to build a Monte Carlo simulation model that does 10 iterations on the interest rate tree. I need to identify the interest rate given a sequence of moving up and down the interest rate tree. I ...
- 1
2
votes
1
answer
291
views
What are the practical costs of repo for a bond trading desk?
I appreciate what a repo/reverse repo transaction is, but I'm struggling to understand exactly how the cost of funding trades via repo works from a practical point of view for a bond trader.
Current ...
- 419
4
votes
1
answer
163
views
Australian banks funding
"Typically, Australian banks pay a small premium to swap foreign currency into Australian dollars. This premium is also referred to as the basis, which is the difference between the implied cost ...
- 341
0
votes
0
answers
729
views
calculating risk free interest rate from put call parity
I'm trying to calculate the interest rate $r$ from the put-call parity.
As per hull, put-call parity is given by the below equation.
$c + Ke^{-rT} = p + S_{0}$
where:
$c$ = current call option price ...
- 101
1
vote
0
answers
73
views
Cost of shorting currencies
I thought cost of hedging/going short on a currency with a forward was given by F/S-1 but it seems the author states 0.25% (see below). Am I missing anything (transaction costs, balance sheet costs, ...
- 341
0
votes
0
answers
3k
views
Yield-to-maturity (YTM) vs effective annual rate (EAR)
If the yield-to-maturity (YTM) on a bond is 5%, is the effective annual rate (EAR) on the cash flows associated with the bond also 5%?
I know that YTM does account for the present value of a bond's ...
- 1
2
votes
0
answers
302
views
Swaption extrapolation
I have some ATM swaption volatilities with the following characteristics:
(-IBOR) payment frequency: 1M
Underlying swap maturities (tail): 1Y, 2Y, 5Y, 10Y, 15Y and 20Y
Swaption expiries: 1M, 3M, 6M, ...
- 21
0
votes
1
answer
114
views
FX futures valuation under negative rates
Market participants use negative interbank rates (LIBOR JPY/CHF) for the valuation of FX futures. Does this make any economic sense?
Positive rates in valuation formula indicate opportunity cost of ...
- 1
0
votes
2
answers
326
views
Carry trade question
Usually carry trades involve borrowing in a low yield currency and invest in a high yield currency. For example, I borrow dollars and invest in Brazilian real. I then use a rolling FX swap to hedge ...
- 341
3
votes
0
answers
99
views
€str rates lower than ecb deposit yield
I have the following question :
How can €str rate be lower than ecb deposit facility rates (deposit yield) ?
Why would a bank lend money at that rate ?
Thank you for your answers
Edit : for instance ...
1
vote
1
answer
269
views
Japan benchmark rates
Can you please confirm on the following?
The difference between TONA (also called TONAR), JPY Libor, TIBOR is that:
JPY Libor, TIBOR are based on quotes from panel banks. The difference between them ...
- 341
0
votes
2
answers
211
views
Best way to lock in margin rate via hedging
I'm currently paying a 1.25% margin rate. This rate is based on the Fed Funds rate plus a margin. I would like to hedge against the possibility of this margin rate increasing. What is the best/...
2
votes
2
answers
697
views
Risk-free interest rate for option pricing from treasury yield curve rates
I am experimenting with an implementation of the Black-Scholes valuation for call options, and ran into the following questions:
Black-Scholes pricing requires a risk-free interest rate. What is '...
- 23
0
votes
0
answers
46
views
Brazil FX market "cupom cambial" [duplicate]
I am trying to understand the role of cupom cambial (onshore dollar rate) in relation to the BCB swaps which are domestic NDF settled in real.
"The cupom cambial is priced in basis points as an ...
- 341
3
votes
0
answers
370
views
Implementation of solvers for curve construction
I'd be really interested to hear people's experiences of implementing global solvers for curve construction, especially with regard to how robust the approach is in practice, numerical performance, ...
- 139
-1
votes
1
answer
86
views
Money market yield question
Assuming the 92-day and 274 day interest rate is 8% (act/360, money market yield) compute the 182- day forward rate starting in 92 days (act/360, money market yield).
1)7.80%
2)8.00%
3)8.20%
4)8.40%
...
0
votes
1
answer
131
views
Are government bond yields usually expressed as yield to maturity (YTM) or annual yield?
If US 10yr = 2%, does it mean if I hold the bond until maturity/for next 10 years the yield is 2% or I get an annual return of 2% for 10 years?
For example the yields in the link:
https://www....
- 341
1
vote
0
answers
53
views
What is the name of this concept/formula?
I stumbled on this not so complicated concept and couldn't figure out what it's called.
I want to buy something that costs $M$ units of money, and have to pay it in $n$ months at a rate of $\frac M n$ ...
4
votes
2
answers
913
views
Gamma of interest rate derivatives
consider an interest rate derivative whose value $V$ depends on $n$ interest rates $r_1, \dots, r_n$.
Hence $V$ is a function in $n$ variables $V(r_1, \dots, r_n)$.
My question concerns the gamma $\...
- 1,446
1
vote
1
answer
99
views
ECB - Two Tier System
It's said the theoretical aim of the ECB Two-tier system (exempt a portion of the excess reserves from negative rates) was designed to:
offset the direct costs of negative interest rates on banks, ...
- 341
1
vote
2
answers
655
views
OIS example in Hull's book
In Hull's book (9th edition), on pages 202-203, there is an example for computing the payoff of an OIS that I am confused about. It says suppose in a US 3-month OIS the notional principal is \$100 ...
- 469
2
votes
0
answers
104
views
What makes modeling interest rate derivatives very difficult compared to equity derivatives?
I understand while equity derivatives require the modelling of stock price at expiry, interest rate derivatives typically require modeling both the expiry and tenor, thus increasing the dimensionality ...
- 21
-3
votes
1
answer
148
views
Calculation of monthly interest and capital repayment in a variable rate mortgage
In my exercise, I take out a 240,000€ mortgage from a bank which I pay off over a period of 30 years. The interest rate is a market index plus a spread. Initally the market index is 1% and the spread ...
- 1
0
votes
1
answer
432
views
IRR with Inflation Rate
I have cash inflows and cash outflows for a 7 year period and my MIRR and inflation rate. That's all the information I have.
How do I calculation the IRR taking the inflation rate into account in ...
- 1
0
votes
1
answer
95
views
Swap Spread Positions with Duration Bias
In practice, how are swap spread positions actually sized and constructed between the two legs? I would suppose the two legs are simply matched in notional terms.
However, in practice, do traders ever ...
