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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116 views

Option on Loan rate

I have been trying to get my head around pricing an option none of the traditional option types fit the structure. I want to get a loan of $100 , 5Y maturity . The lender gives me the following ...
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2k views

Why is the Black 76 model not considered an interest rate model?

The Black 76 model is one of the standard models for interest rate derivatives like pricing caps, floors, swaptions, etc. The Black 76 model is given as $$dF_t = \sigma F_t dW_t$$ so it models the ...
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3answers
861 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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278 views

How to extract parameters in the CIR model from data?

I want to extract CIR parameters from monthly LIBOR data in the EULER-MARYAMA method in MATLAB language. I found the data but I can't extract parameters from it. What is the process? What is the ...
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533 views

Vasicek model problem

I am analyzing a problem where the below is given Vasicek model with risk-neutral dynamics $$dr_t = \kappa (\theta - r_t)dt + \sqrt{r_t} dW_t \quad \quad (1) $$ bond prices $$P(t,T)=e^{A(t,T)-B(t,T)...
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81 views

Price compounding: Swap versus Governments Bonds

There are different rates curve to compound prices. Since the crisis, regulators tends to favor price compounding with swap curves over IR curves deduced from governments bonds (EU regulators, french ...
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1answer
575 views

How to calculate the NPV (Net present Value) in this question? [closed]

A company pays £1,200,000 to purchase a property. The company pays £30,000 at the end of each of the next six months to renovate the property. At the end of the eighth month the company sells the ...
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737 views

Interest Rate Risk - The Greeks

IR Delta and Gamma. Can someone please explain if my understanding is accurate as relates to a 2yr interest rate swap? You are considered to be long Delta in an interest rate swap if you are ...
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1answer
484 views

How to get real interest rate from Nominal spot rates?

I have the nominal spot rates. Based on the Fisher equation , how to get the real interest rate ($r$) and the "expected inflation" ($\pi$) ?
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2k views

difference between caplet and call

I wanted to know the difference between a caplet and a call. In my course (Interest rate models and curves) , we said that a caplet is a call option. Is it really true? Thanks
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55 views

Stressing the going up of LIBOR - Which balance sheet variables to stress?

Analysts expect the LIBOR to rise in the next two years. Hence, all companies that have foreign currency loans will face problems. I am preparing a study on this topic, but data is an extreme issue. ...
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86 views

Immunization: Whats the best way to hedge my short interest rate exposure?

What's the best way to hedge a portfolio against a rise in rates? Portfolio: long bonds different maturities. a) parallel shift b) convex shift (short and long term rise more than mid term) How is ...
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107 views

What is this ratio: expected returns on stock divided by risk free rate?

So this ratio has come up in some work I'm doing and I can't seem to figure out if it is attested in the literature. Here's the setting: Given a risk free rate $r(t)$ and a stock price which follows ...
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2answers
64 views

Incorrect characterization of spot rate?

Is the t in the red boxed $R(t,T)$ supposed to be the same as the S in the green boxed $R(S,T)$?
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1answer
96 views

Why interest rate future does not support fed policy on reducing assets buying?

Using the 3-mon eurodollar interest rate futures, I construct a yield curve each year for 2015-2021 using sampling date from the end of the month. If you graphed this out, you would see that the ...
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2answers
144 views

Different interim balances when calculating annual compound interest different ways

Something interesting that doesn't quite make sense to me. When calculating compound interest using P(1+r)^t, I'm calculating in two ways - one using the day 1 principal balance, and the other using ...
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1answer
223 views

Eurdollar Futures

Trying to understand the Eurdollar market a little better. I understand it's the market for dollar denominated deposits outside the US (not just in Europe). They are unregulated and not subject to ...
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1answer
62 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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112 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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1answer
69 views

stochastic interest rate in binomial pricing model and in continuous models

Is the interest rate allowed to be truly stochastic in the binomial pricing model and in continuous models so that we are still able to switch to the risk-neutral measure? Shreve mentions multiple ...
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1answer
61 views

Zero-coupon bond price under Rendleman-Bartter Model

let's say that I have simulated the interest rate using the Rendleman-Barttermodel, (which is not the best for rates I know) and then I want to simulate paths for the bond paying 1 at maturity: $$...
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1answer
102 views

daycount of the yield curve

Complete characterization of an interest rate requires a few elements: day count compounding frequency the rate itself start date and end date That said, I notice that day counts are never displayed ...
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1answer
58 views

Computing option price with rates only

Hi I am learning about options and came across this example: The spot FX rate AUD/USD is 0.6868, the 6 month ATM implied volatility for AUD/USD is 7.7% p.a., for the 6 month USD deposit rate is 2.28% ...
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37 views

Term structure model for exchange-traded STIR futures and their options

As I understand, models such as the SABR extension of the Libor Market Model are the "standard" for interest rate derivative valuation in OTC markets, where options tend to be European and it is ...
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1answer
113 views

Calculation of Combined IRR

How to calculate combined IRR for two different cost of funds? The emi (Equated Monthly Installment) amount, whether it is calculated separately or based on the combined IRR should be same. I tried ...
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1answer
48 views

Continuously Compounded rate less than a discretely compounded rate [closed]

I'm looking at an example in a well known book and its saying "consider an interest rate that is quoted as 10% per annum with semi annual compounding" The book puts 10% as the semi-annual rate, ...
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1answer
132 views

Ho-Lee short rate model under the Heath-Jarrow-Morton framework

Under the Heath-Jarrow-Morton (HJM) framework the dynamics of the Ho-Lee short rate model are defined as following: $$dr(t)=\theta(t)dt+\sigma dW^{\mathbb{Q}}(t)$$ with $\mathbb{Q}$ the risk-neutral ...
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121 views

Short rate models

On the short rate model in Wikipedia https://en.m.wikipedia.org/wiki/Short-rate_model Why is the first function, the P(t,T) given? This is not the short rate model this is generating prices for a ...
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1answer
117 views

Interest rates, effect on call price

Generally, we assume that an interest rate increase makes the call price more expensive. From my understanding it is because the expected return on the stock price increases. However the interest rate ...
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1answer
83 views

Concentration risk in Rates

What are some good ways to assess the concentration risk for a rates curve or by currency when volumes traded by instrument are not easily available? For ex, if for some currencies, the PV01 at ...
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1answer
292 views

Confusion regarding the risk neutral and physical measures

I may be confused. I am looking at the risk neutral vs. physical measures. We know that knowing the short interest rate stochastic process $r$, a bond maturing at time $T$ can be considered as a ...
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1answer
68 views

Why is LIBOR rate smoother than the US treasury rate?

Compare the daily rate graphs of LIBOR and US Treasury bill, the former is a lot smoother than the latter. Is there any reason for this?
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189 views

Credit Spreads and Relative Value : floating vs fixed bond

I would like to study if, in these weeks during the italian credit crisis, floating govy bonds were more resilient than fixed govy bonds. For each floating issue (CCTS) I chose the fixed issue with ...
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1answer
58 views

Where can I find data on US bank interest rates or 4-week T-bill rates dating back to 1970s or earlier?

Where can I find data showing 4-week T-bill rates or U.S. savings accounts' interest rates from 1960s to present, or 1970s to present?
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58 views

For a market with a bank and risky assets $S_1, S_2$ with different volatility, what should be the short interest rate in this market?

Let there be two assets $S_1$ and $S_2$ s.t.for $\sigma_1 \neq \sigma_2$ $$dS_{1t}=\mu_1 S_{1t}dt+ \sigma_1S_{1t}dB_t \\dS_{2t}=\mu_2 S_{2t}dt+ \sigma_2 S_{2t}dB_t$$ . If there exists a bank, what ...
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1answer
54 views

Recreating / Extending Bond Time Series

I am trying to analyse historical yield curve dynamics within an across countries and step one is extending / recreating historical yields and/or prices. The challenge is this: lets say a 10 year ...
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1answer
391 views

Fixing Rate in Quantlib

While pricing Interest Rate Swap, I am providing Fixing rate for historical date using "addFixing(date, value)" function. But when I am trying to change value it is not happening and picking up old ...
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1answer
239 views

Modelling interest rate

Hi I want to model two stochastic integrals in Matlab, which is given by $ x(t) = x(s) e^{-a(t-s)} + \sigma \int_s^t e^{-a(t-u)} dW_1(u)$ $y(t) = y(s) e^{-b(t-s)} + \eta \int_s^t e^{-b(t-u)} dW_2(...
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1answer
786 views

Fixing date, start date, end date in interest rate derivative valuation?

I was reading a technical report by Hagan, which can be downloaded here on the valuation of accrual swaps and range notes. It caught my attention that in the valuation he comments this: Consider ...
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1answer
939 views

What rate to discount tax shield

On the appendix for Chapter 19 of Principles of Corporate Finance (BMA), it discusses the topic of "Discounting Safe, Nominal Cash Flows", in which case they argue that However, suppose we ask ...
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114 views

Clarifications about the “quotations” of Treasury Bills and Treasury Bonds

Good morning. I would like to ask you some clarifications about the "quotations" of Treasury Bills and Treasury Bonds. Quoting "J.C. Hull": In general, the relationship between the cash price and ...
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476 views

From continuous compounding to simple compounding - convexity adjustment

I have derived the convexity adjustment expression for futures rates using the Ho-Lee model, to arrive at the following: $$ ForwardRate = FuturesRate - \frac{1}{2}\sigma^2T_1T_2 $$ where $T_1$ refers ...
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202 views

Clarification on the Black-Derman-Toy model regarding measuring time and notation

I'm self-studying BDT and I'm having some difficulty with what is meant by the "short-rate volatility parameter for the first year" and "the short-rate volatility parameter for the second year," as in ...
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2answers
441 views

Calculating 3 month libor from 1 year libor?

Is there a way to calculate the four 3-month LIBOR rates (spot and forward) given a 1-year spot LIBOR rate and a 1y1y forward LIBOR rate?
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667 views

Swaption Price with Negative Swap Rate

To price Swaptions, I use the Black '76 model. I'm trying to update the model to handle negative interest rates. One such approach to doing this is detailed here. In particular I'm interested in the "...
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2answers
379 views

Pricing a Vanilla swap between coupons; What rates to use?

Vanilla Swap question. Entered into a 5Y fixed for floating HUF swap. Fixed is annual coupons, Float is semi-annual coupons. 1 month later I want to price it. I set up my future values for Fixed ...
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163 views

Interest rate models

I'm studying by myself how to model interest rates. Is there any database in which I can find accurate data for indices like Libor, Euribor, Eonia etc?
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474 views

what data to use to compare the interest rate among different currencies?

Very new to fixed income signals. I am a little confused about which data to use to compare interest rate among different currencies. For example, I am interested in compare interest rate in the ...
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312 views

Cash flow diagram, interest rate inflow series

I have a econ midterm coming up soon and stumbled upon this question. My approach is: 2C=800/(1.12^2)+1200/(1.12^6)=125.71 or C=1245.71/2=622.85 But I have a gut feeling this is wrong. I believe the ...
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758 views

Total return index for interest rates (EURIBOR 3M)

I would like to calculate a daily total return index for the EURIBOR 3M. • Should I freeze at the beginning of each qurter die rate? (With this methology the developing of the index depends on the ...