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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20 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
33 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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1answer
61 views

How does one calculate the duration of a cash flow

The question reads: A firm has liabilities as follows: £2,910 at time t = 0 and £7,501 at time t = 4 (time is measured in years). On the asset side the firm has two payments, each for £5,000, at time ...
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Does banks' profitability really suffer under low interest rates

It is always said that European banks suffer, amongst other things, from the low interest rate environment governing the Eurozone. And that in a rising interest rate environment, banks' profitability ...
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Finding the redemption yield of a bond given a capital gains tax

Let's say a bond has a face value of £$100$ with semi-annual coupons at a rate of $3$% p.a which is redeemable at par in $10$ years. Assume an investor purchases the bond for £$92$ on the day it is ...
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31 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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21 views

Average interest rates by currency (Basel SRP98)

Can anybody confirm how the average interest rates by currency is calculated as per Basel SRP98? Please scroll down to 98.57 to see the table for different currencies. Step 1: generate a 16-year ...
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4answers
1k views

Why does the ultra long-end of a yield curve invert?

The shape of the yield curve (at least in the GBP Rates market) is upward sloping from the front end up to the long end (i.e. 30y), but then begins to become downward sloping as we go beyond 30y and ...
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1answer
22 views

How to understand interest rate bid/ask and apply client mark-up in Tom/Next Rollover Swap Point Calculation

When I am reading materials in swap point calculation for FX Tom/Next Rollover, I am confused with the market interest rate bid/ask. Using an example: I traded on ...
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3answers
99 views

Why do higher interest rates increase the value of the currency?

I've been trying to study about interest rates and foreign exchange. First of all when people say interest rate in this context do they mean interest rate set by the central bank like federal reserve (...
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1answer
54 views

Interest rate equation from bond price?

If a zero coupon bond price at time $t$, with maturity $T$ ($t<T$), is denoted by $B(t;T) = B(T;T) e^{(-\int_{t}^{T} r(s) ds)}$ where $r(t)$ is a known interest rate. How does this transform ...
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1answer
45 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
113 views

Stochastic process for interest rates allowing negative values

The Cox-Ingersoll-Ross process for the short term interest rate r(t) does not allow r(t) to become negative, but short-term rates are negative in much of the developed world. To account for this, do ...
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2answers
77 views

Which curve does the interest rate risk fall in?

For example, Australian government issues a bond denominated in USD currency? Which curve does the interest rate risk fall in? Australian Gov Curve or USD Gov Curve?
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19 views

Portfolio Values based on reference interest rates

How do I approach the following question? A portfolio has 100 million invested in equities. It has also transacted an interest rate derivative issued by counterparty X, which the value is 0 if the ...
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1answer
70 views

Duration. Floating rate note

I don't understand why the duration of a floating rate note equal to the time to the next coupon payment? Please, look at my calculations. Here: P - is price at moment 0.
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84 views

Ito's lemma for special case

Assume a HJM framework with the same Brownian motion driving the dynamics for every tenor. $$ df(t,T) = \alpha(t, T)dt + \sigma(t,T) dw_t \,, $$ with $\alpha(t, T) = \sigma(t,T)\int_t^T \sigma(t,s)ds$....
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1answer
46 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
46 views

Swap Pricing - Using forward rates vs using par bond after first floating payment

There seems to be two different methods I have come across for valuing a Interest Rate Swap - specifically the floating leg. One method described by Hull: incorporates the cashflow from the first ...
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1answer
74 views

Bond-price dynamics in the Vasicek model

Hello I am studying about interest rate modeling There is one good source about Vasicek (link: https://web.mst.edu/~bohner/fim-10/fim-chap4.pdf). However there is one equation that I try but unable ...
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2answers
257 views

Interest Rate Models cheat sheet - Need for advice

I'm trying to get through the litterature of interest rate models for some time now. As I don't have any experience working with them, I started looking for some kind of a cheat sheet that would ...
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36 views

Deriving the series for federal funds rate expectations using federal funds futures

I am trying to derive the monthly series from 2000-2019 of the expectations of federal funds rate based on federal funds futures. How should I proceed? Where to look? Is it possible?
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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
284 views

When interest rates go up, why do call option prices go up?

I studied that generally speaking, interest rates and share prices have an inverse relationship. When interest rates go up, share prices go down. If interest rates go up, wouldn't people be less ...
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0answers
40 views

Equivalent of recovery rate

I'm trying to understand the functioning of "recovery of face-value" approach. Let $V_t$ the fair-value, that is the price that the holder of a defaultable bond must pay for hedging of default of ...
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1answer
88 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
53 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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46 views

Wave Method and Implied Duration

I am pricing an MBS under three different rate scenarios: a base case, +5bps and -5bps I compute partial durations on the base case using the wave method (P. Hagan: Calculating Delta Risks and Hedges ...
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0answers
61 views

What are good TEXTBOOK on stochastic volatility and interest rate theory?

I wanted to learn stochastic volatility modelling and interest rate modelling. On this site, a answer recommended me the books "Stochastic Volatilty Modelling" by Lorenzo Bergmo and "Interest Rate ...
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2answers
70 views

Interest Rate Assumption (Ornstein - Uhlenbeck Process)

Why can we assume that interest rate is stationary (identically distributed), Gaussian (has multivariate normal distribution), Markovian (the future is determined only by the present), and continous ...
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1answer
30 views

Multi-factor vs Single-factor interest rate model for XVA / CCR

When calculating XVA or Counterparty Credit Risk (CCR), you can choose to simulate your interest rate with a Multi-factor interest rate model or a Single-factor interest rate model. What are the pros ...
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1answer
72 views

what are the underlying transactions for SOFR?

Recently I am reading about SOFR (Secured Overnight Financing Rate), which is projected to replace LIBOR to be the reference for risk-free rate in the market. But I still don't understand or imagine ...
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1answer
82 views

How to prove martingality of forward rate under T-forward measure

Let $P(t,T)=\mathbb{E}_{Q_{R}}[e^{\int^{T}_{t}r(u)du}|\mathcal{F}_{t}]$ be the price of a 1-euro zero-coupon bond with maturity $T$ and $r(u)$ the interest rate process. Consider the the forward rate $...
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28 views

Stochastic process with determinstic frequency of regime changes

Suppose that I have an OU process. For instance, assume that I want to model the interest rates. Suppose that regime change is known ex ante, and is deterministic in terms of frequency (For instance, ...
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1answer
118 views

Proof of the Hull & White Model calibration

I have a question about the demonstration of the formula which states that: If we have an Hull & White Model for the short rate diffusion such that Then the model is fully calibrated if and only ...
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1answer
55 views

Transforming non-normally distributed interest rates for OLS regression

I am studying the effects of short- and long-term interest rates on bank risk-taking in the Euro zone countries. To analyse the effects, I will use, amongst other, an OLS regression. However I have ...
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64 views

What are the go-to textbooks for advanced quant finance topics? [duplicate]

Credit risk, interest rate modelling, volatility modelling. What are the go-to books for each of these 3 topics in quant finance? The target audience should be someone who understands the basics of ...
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1answer
122 views

What's Hedge Curve Template

what's a Hedge Curve Template (HCT)? How does it help value a bond? It appears to me it normally is used together with another curve where x,y-axis being maturity dates and discount factors ...
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27 views

Risk neutral interest rate calibration

I've only worked with RW model before but not RN interest rate models, so I'm looking for some practical insights on how RN calibration is done for interest rate models. Let's say I want to start ...
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0answers
34 views

Pricing call option on bond under CIR model by simulating noncentral chi square distribution

In the original paper of CIR model, there is a pricing formula about call option on bond $$ \begin{array}{l}{C(r, t, T ; s, K)} \\ {=P(r, t, s) \chi^{2}\left(2 r^{*}[\phi+\psi+B(T, s)] ; \frac{4 \...
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56 views

Why don't we build the discounting curve and projection curve from bonds

We know that we always build the discounting curve and projection curve from money market instruments, index Futures, interest rate swap and OIS Libor swap (depends on the period). But why don't we ...
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53 views

Does Vasicek interest rate model had any derivation that follows from a list of assumptions?

I can't find that anywhere online and It doesn't seems to me that this model originated come from intuition or some human motivation but rather it is coming from computerized curve fitting as all the ...
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1answer
53 views

Cross currency swap basis with USD added on the covered interest rate parity (CIP)

We know the adjusted covered interest rate parity (CIP): $$Forward = \dfrac{1+r\cdot\tau+b}{1+r^*\cdot\tau+b^*}Spot$$ Here $r/r^*$ is the risk-free foreign/domestic rate and $b/b^*$ is the cross ...
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1answer
31 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
66 views

Why financing costs are ignored in capital budgeting of projects?

Any finance textbook I have encountered including CFA materials states something like this: "Financing costs are ignored. This may seem unrealistic, but it is not. Most of the time, analysts want to ...
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1answer
92 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
98 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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1answer
39 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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0answers
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How does this transformation for Euler Scheme in mean reverting SDEs alleviate instability?

I saw this text in the book - Interest Rate Modelling by Andersen volume 1 on Page 112: I am unable to understand: How does instability arise when we use the Euler scheme on X(t)? What change does ...
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0answers
31 views

Discrete term structure models - generalized procedure to ensure positive probabilities across multiple measures

Question: Is there a generalized procedure for building a discrete (e.g. binomial) term structure model with risk-neutral branching probabilities that ensure positive probabilities under alternative ...