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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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From BS formula how to show Euro-call values go up and Euro-put values go down with interest rates?

The BS formula gives, as quoted from Wikepdia: $${\displaystyle {\begin{aligned}C(S_{t},t)&=N(d_{1})S_{t}-N(d_{2})Ke^{-r(T-t)}\\d_{1}&={\frac {1}{\sigma {\sqrt {T-t}}}}\left[\ln \left({\...
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39 views

Relationship between hike in interest rate and drop in treasuries yields

How does a hike in interest rate results in drop in yields of treasuries? My understanding was that when interest rate rises, investors would sell-off bonds, which would result in increase in yields.
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100 views

Call option prices in terms of maturity with negative interest rates

let's assume that interest rates are constant, $r$. When $r\geq 0$, we can see that if $T_1<T_2$ and $C_1$ (resp. $C_2$) is the price of a call option on a non-dividend paying stock with maturity $...
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248 views

Parametric estimation of risk-neutral density/implied distribution

since a long time I'm struggling with a particular question regarding the parametric estimation of the risk-neutral density (or implied probability) from option prices. I want to pursue the ...
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19 views

$\sigma$-indepencene in affine multi-factor model for interest rate derivatives

The model here is affine two-factor model for interest rates. Let $p = p(r, \sigma)$ denote bond prices which take the usual exponential form. Let $r$ have some $Q$ dynamics, and let $\sigma$ be the ...
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1answer
935 views

Price of bond future, given a specific interest rate?

I'm interested in calculating what a theoretical price of the ZB or UB(Ultra Bond) futures would be priced at, given an interest rate of 1%. Or 0% If the 30Y interest rate is around 1%, what will ...
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115 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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934 views

What is the risk-free rate of a precious metal, e.g. gold?

The risk-free rate of a x-currency denominated instrument can be determined from treasury bills, interbank borrowing rates (e.g. LIBOR), overnight index rates or interest rate swaps. What instrument ...
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343 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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1answer
145 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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76 views

Continuously matured risk free interest rate

I read that in BS model it is advised to use as risk-free rate that one of the area you are trading(T-Bill in america, German in Europe...) that have the same maturity as the option. In the derivation ...
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58 views

Is there an open architecture API or excel solution for calculating and adjusting bond pricing?

Is there an open architecture API for calculating and adjusting bond prices? I am looking to adjust bond pricing on OAS or adjusted spreads to various indices and need a tool to process large amounts ...
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4answers
5k views

Which risk-free interest rate to use in Black-Scholes equation

Sorry but i'm new in quantitative finance. According to BS derivation the risk-free interest rate is the rate to wich the rate of a particular investment tends when the risk tends to zero. Suppose i ...
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99 views

how to define the risk neutral measure when the interest rate itself is stochastic? [closed]

Following Shreve's notation, $d(e^{-\int_{0}^tR(s)ds}X(t))=e^{-\int_0^tR(s)ds}\sigma(t)\Delta(t) S(t)(\frac{\alpha(t)-R(t)}{\sigma(t)}dt+dW_t)$. In order to make $d(e^{-\int_{0}^tR(s)ds}X(t))$ a ...
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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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6k views

Best method for interpolating yield curve? [Multiple questions]

I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run ...
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Obama's lowering mortgage ins rates makes no fiscal sense, because the Fed just raised its rates for the first time last year. Right?

Background: This is a follow up from this question, regarding Obama's lowering of the mortgage insurance rates 11 days before Trump was inaugurated (not to go into effect until week after Trump became ...
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Jamshidian's trick for Swaptions

Following Brigo$^1$ p.77, we can decompose the price of a swaption as a sum of Zero-Coupon bond options (Jamshidian's Trick). To do so, the authors suggest to find $r^*$ the value of the spot rate at ...
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1answer
112 views

Why can't/doesn't the Fed adjust the federal funds interest rate continuously?

Maybe the question I'm asking doesn't make sense-- but this is something I've wondered about since I learned about the Fed in high school. The media typically talks about Fed interest rate changes as ...
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3answers
4k views

Calculate OIS rate 3 months, 1 year

I don't know if there are any similar posts in this forum but I’m trying to describe below all things that I understand about OIS rates and Libor rates. Please correct me if I’m wrong somewhere. I am ...
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1answer
119 views

Textbook for US Treasury Bond / Notes Futures

Is the text The Treasury Bond Basis by Burghardt still the authoritative source on this topic? The most recent edition was published in 2005. I think that, based on the contents and others' ...
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2answers
363 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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2answers
479 views

How is this probability (45%) of Fed raising rates 3 times in 2017 calculated from Fed Funds market?

The probability of the Fed raising rates 3 times in 2017 is above 45%. What data and formula is used to calculate this probability? This Financial Times article is published on 17Dec2016. She ...
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2answers
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formula for physical DV01 of interest rate swap

Most answers to the question "what is the dv01 of an interest rate swap" are along the lines of: "compute the difference between the price of the swap and its price using a curve perturbed by 1 basis ...
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0answers
781 views

Free Data Source for Credit Spreads?

Credit spreads are a key economic indicator. They are the difference between yields on corporate and government debt. They are a measure of confidence in the private sector, they provide insight into ...
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1answer
81 views

Do we need a model for dynamics of IR to price a vanila swap?

This question has been asked in several different forms, and the answer given seems to be always "no" because we can "simply read off the yield curve". However, since the yield curve (or "a yield ...
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1answer
383 views

Calculation of Weighted Interest Rate based on Outstanding Debt

I would like to know what's the way on how to calculate the weighted average interest rate for a loan portfolio properly, especially when looking at periods shorter than a year. The basic definition ...
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1answer
217 views

Closed- solution for Convertible bond price two factor model

I am trying to find the closed- solution of convertible bond $V(s,r,t)$ under Vasicek model of two factor model of PDE shown in below link Ito lemma of Convertible Bond under Two-factor Model ...
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1answer
89 views

APR and Term to Principal Repayment Schedule Approximation

Is there any established "industry standard" to obtain an approximation for the expected principal repayment schedule for a given loan amount, term in months and APR with monthly payments ? I ...
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1answer
451 views

Effective Annual Rate (EAR) calculation from periodic rate of invoice credit

I'm working on a finance class related problem, concerning the Effective Annual Rate (EAR) of an invoice credit rate. The standard formula of the EAR is: $ EAR = \big(1 + \frac{APR}{m}\big)^{m}-1$ ...
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Vol specifications under Heath Jarrow Morton framework

What are some of the common forward vol specifications under HJM framework used in the industry. I guess most common would be 2 and 3 factor models, but any pointers to more details would be very ...
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184 views

How to find time of mean reversion of an interest rate model

In the Cox–Ingersoll–Ross model, we can find the half-life of the interest rate as: half-life= log(2)/speed of reversion to equilibrium rate. Is it valid to ...
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1answer
58 views

Relation between Libor market model and Black76 with time-dependent vola

The Black76 model uses a lognormal process to model the forward rate $L_1(t)$ from $T_1$ to $T_2$ at time $t$, $$dL_1(t) \ = \ \mu(t) L_1(t) dt + \sigma(t) L_1(t) dW_t$$ By switching to the $T_2$-...
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1answer
442 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
426 views

Falling Futures prices positively correlated with interest rates

I'm having trouble understanding how Futures are worth more than Forwards when price and interest rates are positively correlated but both declining. For instance, a Future with losses of -5 at T(n-...
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1answer
131 views

Zero-coupon Loan Investment [closed]

Zero-coupon default-free interest rates maturing over the next five years are listed below (in percent per annum, continuously-compounded): Maturity Years -- Yield 1 --------------------1.9 2 ------...
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74 views

Difference between Zero-Bond-Curves and Term-Structure Models?

I'm trying to model a fixed-income securities (in specifc a loan with prepayment) but I got confused in some general aspects. So if I want to model a simple loan, I could just use a simple present ...
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135 views

Implied Equity Volatility under Stochastic Interest Rate

I would like to draw some general conclusions for the effect of stochasticity of interest rate on the implied volatility of a European call of a stock. Below I show, trivially, the implied volatility ...
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1answer
245 views

Short rate models (stochastic)

I want to make a quick reference or some pages, that contains short rate models . I know some models but I am not sure that ,this list is complete ...please help me to $\textbf{improve}$ this list ....
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0answers
401 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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180 views

Pricing interest rate options in emerging markets

I've been thinking how to price the early payment of mortgages in banks from emerging markets, where swaptions/caps/floors aren't available, and how to hedge this kind of options. At first I thought ...
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5answers
7k views

What is a regime switch?

I've come across the term regime switch in volatilities when reading about the modelling of interest rates but could not find a definition for a regime switch and what a regime is. Can somebody give ...
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1answer
47 views

The weight of interest rates

Why are average interest rates often weighed by loan (and deposit) sizes? Since the size and interest rate of a loan are function of each other, I expect the resulting statistic to be hard to ...
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1answer
2k views

Where can I find open swaption implied volatility data?

Anyone have a good place to find interest rate swaption implied volatility data? Does Bloomberg's python API allow access?
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1answer
1k views

Calculating Implied Forward Rates from Eurodollar Futures Quotes

I'm trying to calculate the implied forward rates of the Eurodollar (USD) curve, knowing that the Eurodollar curve is supposed to be a mirror of the yield curve (else arb). I have this formula for ...
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3answers
213 views

Is a bondfuture an IRD or a Credit Derivative?

I need to categorize a BondFuture trade in one of the five major asset classes and I am not sure if it should put it to the interest rate asset class or the credit asset class. A quick (and dirty) ...
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1answer
1k 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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1answer
695 views

Why does one-factor short-rate model tend to produce parallel shift of the yield curve?

I understand that one factor short rate model models the instantaneous rate given any moment in time. Can anyone explain how to derive a term structure from a short rate model and show that one-factor ...
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0answers
241 views

Hull White 2 factors and non Markov interest rates

I am studying the calibration of the 2 factors Hull White model on Brigo and Mercurio's book. They point out that, using cap volatilities, the value of $\rho$ is almost minus one and this means that ...
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141 views

Pricing with Vasicek model on basket of credit spreads

I would appreciate help with a valuation of a fixed income derivative, with an embedded exit option. Summary: Goal is to provide valuation of a fixed schedule of quarterly cash flows with an option ...