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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).

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1answer
53 views

Cox-Ingersoll-Ross Zero Bond Put Option

according to Brigo & Mercurio (2006): But how is the Zero bond Put of the CIR model? I couldn't find any information about that. Thanks in advance. Regards Chris
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1answer
50 views

Hedging a trade for PCA component neutrality

Suppose I am given a set of financial instruments, e.g. {1Y, 2Y, ..., 30Y} interest rate swaps or {Barclays, Lloyds, .. } FTSE100 companies. It doesn't matter which so let's go with IRS. I have ...
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69 views

cashflow for floorlet option on 1 month Libor under Vasicek

I have to figure out the cashflow for a floorlet option written on 1 month Libor under Vasicek model by considering yield curve power series expression and bond pricing equation: Has anyone an idea ...
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1answer
338 views

Calibration of Cox-Ingersoll-Ross process that hits zero (Feller condition violation)

I'm considering a Cox-Ingersoll-Ross (CIR) process $$ dx_{t} = \alpha\left(\theta - x_{t}\right)dt + \sigma \sqrt{x_{t}}\,dW_{t}\,,\qquad \alpha,\beta,\sigma > 0 $$ which by assumption has $2\...
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2answers
154 views

Calculating spot rates from forward rates

I am working on a problem where I am trying to calculate the forward rates from two different spot rates. I have the following: ...
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3answers
145 views

Is EONIA swap rate really credit risk free?

I have a question linked to the EURIBOR – EONIA spread (or OIS LIBOR spread). I understand that the EURIBOR - EONIA spread is a credit risk indicator of the interbank market. There is something I ...
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1answer
121 views

Bootstrap ESTER and SOFR curves with Quantlib Python

Is it possible to bootstrap the new ESTER and SOFR term structures in Quantlib? More in general, does the process work as the usual one? Given these are simple indices that are published on a daily ...
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30 views

computing theta of black normal model?

I've been trying to create a black normal model and have used http://janroman.dhis.org/finance/Swaptions/normal%20swaptions.pdf as a guide. I am trying to validate the theta formula in this paper - ...
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1answer
723 views

Hedging with interest rate futures, different duration

This is from Hull, problem 6.16. Suppose that it is February 20 and a treasurer realizes that on July 17 the company will have to issue \$5 million of commercial paper with a maturity of 180 days. If ...
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1answer
42 views

How would you use FRAs to find out how much Central Banks would cut/hike by?

Let's say you have The FRAs 1x4F, 2x5F, 3x6F, 4x7F, 5x8F... (meaning 3 months rate today, 3 months rate in 1 month, etc..) at 5.5, 5.5, 5.6, 5.55, 5.55. Assume today's date is 20/09/2019. You also ...
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1answer
109 views

Practical purpose of overnight repos

I know this might not be a very quantitative question, but I figure this is the most relevant place to ask this. Over that last few days, there has been a lot of news from the repo market, for ...
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3answers
112 views

Bond strategy in rising rate environment

During a period of rising interest rates, it makes sense for investors to either swap out their longer term bonds for shorter ones, or simply invest in shorter maturity bonds in order to reduce ...
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2answers
127 views

Instantaneous forward rate within the HJM framework

within the HJM framework, the dynamics of the instantaneous forward rate are defined by: $$f_t(T)=f_0(T) + \int_0^t\alpha_s(T)ds+\int_0^t\sigma_s(T)dW_s$$ or in differential form: $$df_t(T)=\alpha_t(...
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0answers
67 views

Understanding APR via programming [closed]

I am trying to better understand different types of interest rates. However, I am having difficulties complete, consistent and pedagogically-efficient explanations online. Thus, I have decided to ...
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0answers
18 views

Formulating Deposit Rate Sensitivity to Market Rate Changes

I have historical deposit rate data for a specific bank. I want to determine the sensitivity of deposit rates to market rate changes (I'll be using Fed Funds rate). My question is, what would be an ...
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1answer
76 views

Interest rates compounded monthly [closed]

Suppose the quoted APR is $r_0 = x-1$ and interest is compounded monthly; Am I correct in saying the formula for the monthly interest rate $r$ is: $$r = (1+ (\frac{r_0}{m}))^m -1 $$ Is it also ...
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2answers
88 views

Delta one trading: dependence on repo rate?

I have heard a delta-one trader mentioning the dependency of its activity on interest rates, dividend yields and repo rates. While I can understand the exposure he has to interest rates and dividend ...
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3answers
1k views

Effect of interest rate on options prices

This might be another basic derivatives question. When interest rate rises, stock prices generally fall. Assuming an option's underlying is a stock, this should lower the option's price as well. ...
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1answer
73 views

Required adjustments for stressed yield curves

I was looking at Basel proposed interest rate shocks. Using the standard US Treasury Yield Curve for the period starting from September 2017 to August 2019, I was able to construct Steep and Flat ...
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2answers
93 views

Stress testing fixed income Yield curve with Nelson Siegel

I am attempting to stress test the Zero coupon Yield curve using The Nelson Siegel model as described in the following papers : Generating Yield Curve Stress-Scenarios Representative Yield Curve ...
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3answers
118 views

Why repo rate above federal funds rate while appears less credit risk

I think this will be an easy question for practitioners but going through several websites & papers is causing more confusion than anything else. So here goes: The effective federal funds rate is ...
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26 views

Markovian short rate in HJM framework

In Bjork it is proven in proposition 20.5 that a forward rate dynamics: \begin{equation} f(t,T) = f(0,T) + \int_0^t\alpha(s,T)ds + \int_0^t\sigma(s,T)dW(s) \end{equation} imply a dynamics for the ...
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3answers
2k views

Estimating Parameters - Vasicek

The Vasicek model for the short rate $r_t$ is given by the SDE $$ dr_t = \alpha(\beta - r_t)dt + \sigma dW_t, $$ where $W_t$ is a Brownian motion under the physical measure. I'd like to compute bond ...
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1answer
132 views

repo rate v.s. reverse repo rate

From a book, I read that the repo rate is usually higher than the reverse repo rate. i.e., the rate of financing a long security position is higher than the rate to lend cash using securities as ...
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1answer
371 views

Could banks move to continuous (rather than overnight) funding?

For a long time, the dominant tenors for money market and FX instruments were 6 months and 3 months, and banks slowly moved to commercial trades at those tenors but funding overnight. If this is a ...
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47k views

how to derive yield curve from interest rate swap?

According to some textbooks, to derive the yield curve, quote overnight to 1 week: rates from interbank money market deposit, 1 month to 1 year: LIBOR; 1 year to 7 years: Interest Rate Swap; 7 ...
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3answers
815 views

Calculating FRA rates

Let's assume I constructed usd libor 3M curve setting 1M rate=3M rate (so the curve is flat between 1M-3M). Will 1x4 FRA rates be good if calculated from such curve?
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0answers
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Average interest rate [duplicate]

Earlier I asked a question about average FX rate. I'm building simple linear model and need to use monthly data. I have a yearly interest rate that changes daily. How to aggregate it over the month, ...
4
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1answer
117 views

Implied interest rate using put-call parity

In the process of asking this question, I acutally found the solution. I still let this post open if it can be interesting to someone else and have added a related question at the end. I want to ...
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2answers
77 views

How do the following aspects lead to U.S. Repo shortfalls

A major theme in the markets this past week has been the repo rate hikes and the sudden disappearance of liquidity. Although most are confused as to the main reason, there seems to be a consensus on ...
3
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1answer
141 views

Hedging EURUSD with negative rates

I was reading an article and i saw this : Fund managers based outside the eurozone can profit from buying Europe’s negative-yielding government debt thanks to an uplift from hedging the currency. ...
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1answer
56 views

impact of bond futures conversion factor on calendar spread trading

i have a quick question about conversion factor and his implication in calendar bonds roll trading. I go short on a calendar roll (short front+long back) which has the same cheapest to deliver. The ...
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2answers
184 views

How do markets price an interest rate rise?

It is common to see phrases like Markets priced in a 68 per cent chance of a rise in UK interest rates at the next meeting, up from 48 per cent before the June decision was announced This example ...
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1answer
67 views

Interest Rate Swap curve: CMS vs. OIS?

I'm working on a project where we're trying to create a database model where we can (daily) update collected data in order to make RPA predictions. We received data from Interest Rate Curves called ...
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1answer
32 views

Definition of interest rates in binomial tree model

I'm studying financial mathematics from Shreve's text. I have two problems. 1) "for a binomial tree with three steps, where $S_0=20$, $u=1.05$, $d=.95$ and continuously compounded risk-free interest ...
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1answer
27 views

PV of security with interest-dependent cash flows

I struggle with the following exercise, where the correct answer is supposed to be "no": A riskless security with cash flow $C_1, C_2, \dots, C_n$ has a market price of $\sum_{i=1}^n C_i\,d(i)$. ...
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1answer
116 views

Bond Option Hedging

(My question) Please show me how to solve from (2) to (4) with computation processes. These are too difficult to solve. Thank you for your help in advance. (Cross-link) I have posted the same ...
2
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1answer
59 views

Can someone provide a good definitive explanation for rho in relation to option risks?

I have a pretty good understanding of option risks except for one thing, rho. Unfortunately, interest rates tend to have a small effect on option prices, and thus most literature tend to just gloss ...
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1answer
2k views

Shape and geometry of the yield curve

Let the initial yield curve $T\mapsto y(0,T)$ be given for a term structure family of bonds $B(0,T)$ having different maturities. I am trying to figure out the geometric properties of the yield curve. ...
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1answer
58 views

If short rates $r(t)$ do not determine the bond prices $P(t, T)$, then what is the basis for short rate models?

The question title says it all: We know that in general, specifying the short rate $r(t)$ does not specify the bond prices $P(t, T)$. So how can a model for short rates—for example the Vasicek model—...
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2answers
130 views

Interest rates impact on forward prices

In stock option markets, rising interest rates will increase the froward price, causing call values to rise and put values to fall. But my understanding is that rising interest rate will cause stock ...
2
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2answers
57 views

Cumulative Integration with regard to Vasicek Model's Bond Price and its Forward Price

(My Question) Please show me how to compute the following expectation with its computation process. Besides, $B_t$ is S.B.M. $$E\left[ \exp \left( - \int^T_t \int^u_0 \sigma e^{-b(u-s)} d B_s du \...
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1answer
59 views

How to derive the expression for the forward rate?

The following RN dynamics of a ZCB maturing at time is given: $$\frac{dZ(t,T)}{Z(t,T)} = r_tdt + \sigma_Z(t,T)dX_t$$ and the forward rate is given: $$f(t,T,T+\delta) = \frac{ln(Z(t,T)) - ln(Z(t,T,...
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1answer
97 views

How would this 10s/20s steepener work

Say I'm interested in a trade that wants to execute a 10s/20s steepener This is done via a receiver leg on the 10s and a payer leg on 20s Look at the following example (the figures are all ...
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0answers
68 views

Quantlib Bond PV01 by Tenor

Having built a fixed rate bond object, and looking at here and here , is there any way of retrieving the NPV impact of a repriced bond by bucket/tenor of the Spot Curve instead of getting a simple NPV ...
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1answer
71 views

What does 5 year OIS actually mean?

I am aware that OIS is the new reference/risk-free rate for collateralized cashflows. OIS is by definition an overnight rate (annualized, I assume). So once I have constructed my OIS yield curve, what ...
2
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1answer
68 views

The Riccatti equation for The Cox-Ingerson-Ross Model

(My Question) I went through the calculations halfway, but I cannot find out how to calculate the following Riccatti equation. Please tell me how to calculate this The Riccatti equation with its ...
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0answers
55 views

Arbitrage pricing models

I have been reading Wu's Interest rate modeling and in his chapter on the HJM model he says that With arbitrage pricing models, the prices of the basic instruments are treated as model inputs ...
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2answers
376 views

Hedging amortising interest rate swap with vanilla swaps

Is it possible to hedge an amortising interest rate swap (linearly decreasing notional) with a series of vanilla interest rate swaps? With the amortising swap originated today at par rate and the ...
3
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1answer
81 views

Investor rationale behind inverted yield curve

I just had a question regarding investors/markets rationale behind the cause of the yield curve. Assuming that investors believe that rates will be lower in the future and are pessimistic about the ...