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2
votes
2answers
576 views

Fair swap rate of an amortizing swap

Recently I came across the problem of amortizing swaps. This is an agreement, where fixed payments and floating payments (e.g. 3-months LIBOR + spread) are exchanged based on a notional that is ...
1
vote
3answers
2k views

How to hedge the fixed leg of a swap contract?

I happened to get this question for Fixed Income Swap contract. (let's assume it's it's not cross currency). If the fixed leg is paying 10% interest rate in this contract, but in the market the ...
2
votes
3answers
2k views

Is there an Australian Interbank Rate?

Most widely used Interbank Rates are LIBOR, EURIBOR. Then I read online on SIBOR (Singapore). It says Canda, US are following LIBOR as well. So for Australia, is there a dedicated interbank rate like ...
3
votes
1answer
139 views

Value options when the currency’s risk free rate is negative?

How would you handle a negative interest rate in index/equity options valuation? An example would be negative rates for short term maturities for Swiss Frank (CHF).
2
votes
1answer
327 views

BDT model implementation

I am looking for a nice and readable description of how to implement BDT model: $d log(r(t)) = [\theta(t)-\frac{\sigma'(t)}{\sigma(t)}log(r(t))]dt + \sigma(t) dW$. I assume I already have ...
2
votes
0answers
255 views

Yield Curve Volatility

Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds. Each yield curve has its slope and its curvature, and they obviously change ...
1
vote
0answers
108 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 ...
5
votes
4answers
498 views

Regressor: Nominal return, continuous return or first difference?

Suppose the application is linear models in financial econometrics. If we want to analyze stocks, the standard approach is to take the continuous/log return: $\ln{ \frac{P_t}{P_{t-1}} }$. Suppose, ...
5
votes
0answers
153 views

Replicating portfolio and risk-neutral pricing for interest rate options

For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing ...
3
votes
0answers
230 views

How does one estimate theta in the Ho-Lee model from a yield curve?

I have a yield curve constructed using linear interpolation with data points every 3-months for US treasuries. I would like to use that calibrate a Ho-Lee model, but I can't wrap my head around how ...
1
vote
1answer
382 views

What are current interest rates on senior/junior/mezzanine loans for e.g. real estate developers?

For a case study I have to work on for a university course, about a real-estate-development project, I need to simulate the financing with different proportions of equity (40%), senior loan (35%), ...
2
votes
1answer
138 views

Why for one year (and not two or three) government bonds (there is a spike for Switzerland & Denmark)?

On 10.10.2012, I have looked at the bond-rates and, both for Switzerland and Denmark, there is a discontinuity/spike at 1Y, as per below Switzerland: ON= -0.09, 1W= -0.180, 1M= -0.230, 3M= -0.2, 6M= ...
6
votes
4answers
795 views

Why the interest rate for put-call parity is not constant?

Usimg the put-call parity $C - P = S - K · e^{-rt}$ I tried to estimate the value of $e^{-rt}$, the present value of a zero-coupon bond that matures to 1 in time $t$: $e^{-rt} = (P - C + S) / K$ ...
6
votes
3answers
2k views

Why would a 6M LIBOR rate be significantly above 3M LIBOR, ED futures and swap rates?

Just was just looking at the various interest rates and noticed this: ...
6
votes
4answers
279 views

Government bonds with negative yield

In the recent time-series of bonds issued by (for example) Germany, Austria and France we see an unfamiliar phenomenon: negative yields. This is mainly the issue on the short end of the yield curve. ...
2
votes
1answer
645 views

Calculate the “ten year zero rate” given two bonds with two prices

I have a little question and need some help with the notation. So, the question goes as follows: A bond with a maturity of ten years that pays annual coupons of 8% has a price of \$90. A bond with ...
1
vote
0answers
61 views

Neglect the positive values in negative interest rates modelling?

The magnitude of the negative interested rate should vary correlated with the increase in fixed assets prices and with cross-currency basis spreads. Could their volatility / correlation ...
0
votes
1answer
67 views

Separated software and physical cash flows modelling and pricing to be used with negative interest rates?

The physical cash presence in the final transactions is one of the issues in the presently observed negative interest rates bonds. Such a situation has historically been modelled within the "liquidity ...
11
votes
1answer
758 views

Modelling with negative interest rates

For a project, I am interested to model the impact of recently negative interest bonds on the portfolio. The literature on modelling negative interest rates is limited, and the only theory I could ...
2
votes
1answer
300 views

Question on OIS and fed funds rate

If i am considering the 0-5 year irs spread for the USD market, would it be more accurate to use the fed funds rate or the OIS rate? I believe the OIS rate is calculated based on the fed funds rate, ...
6
votes
1answer
506 views

Implied forward rates puzzle

Here's an interesting cocktail puzzle related to the term structure of interest rates. One of the primary competing theories for explaining the term structure of rates is the Rational Exepctations ...
-4
votes
1answer
193 views

inflation > interest rate? [closed]

Currently, the federal reserve interest rate is 0-0.25%, and the inflation is 2-3%. Does this contradict the no-arbitrage principle? (The arbitrage being: borrow money at 0.25% and invest it in the ...
3
votes
2answers
221 views

Is it true that pricing an IR swap doesn't require any stochastic model but calculation of the PFE of an IR swap would?

Pricing an IR swap doesn't require any stochastic model but calculation of the PFE for an IR swap would require the Hull White Model or any other stochastic short rate or forward rate model. Is ...
6
votes
3answers
2k views

What is a real world example of negative forward interest rate?

As the title says, I am looking for a real world example where a forward interest rate is negative. Theoretically this is not a problem at all, if I look for a 3M forward interest rate that starts ...
4
votes
1answer
234 views

What's the best way to test/validate an interest rate lattice model

I have some implementations of interest rate lattice models. I would like to verify their performance. What would be the best approaches? Currently I compare pricings of some interest rate dependent ...
4
votes
5answers
5k views

Why use swap-rates in a yield curve?

I have a question concerning interest yield curves. Many institutions use the Libor-swap rate curve as a yield curve. Let's be precise and say that we want the yield curve to be the curve that gives ...
13
votes
2answers
780 views

Why isn't the Nelson-Siegel model arbitrage-free?

Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e. $$dX_t=\sigma dB_t-AX_tdt$$ and the spot interest rate evolves by the following equation: $$r_t=a+b\cdot X_t.$$ After solving for $X_t$ ...
4
votes
1answer
4k views

Deriving spot rates from treasury yield curve

I've been experimenting with bond pricing using easily available data (treasury auction prices and treasury yield curves on treasury direct). At first I assumed that I could use the components yield ...
5
votes
1answer
97 views

How to remove the risk element from a set of fixed rate mortgage offerings?

Kept waiting in the bank yesterday, with no paint to watch dry, I found myself staring at the mortgage rates. (These are all annual interest rates): Variable: 2.475% 1 year: 2.90% 2 years: 3.05% 3 ...
8
votes
1answer
413 views

Where can I find data on the interbank lending market?

Where can I find disaggregated interbank lending data (i.e. bank A lends to bank B x money at y rate)? I could only find data on interest rates. I would accept LIBOR market data as well as any ...
6
votes
1answer
138 views

Should we apply practical constraints on the distribution of monte carlo paths?

to limit interest rate paths to a 'reasonable' range (if we could define reasonable). Now we calibrate log-normal skew and mean reversion monthly to robust basket of atm swaptions and in and out ...
5
votes
2answers
332 views

Which interest rate should I use for the discount rate in real-world pricing?

Suppose I want to compute the time value of money (present value, future value, etc). I need to put an interest rate into the calculation. Which real world interest rate would best be used here, ...
3
votes
3answers
677 views

What are the limits of bond portfolio immunization against interest rate changes?

I'm currently reading through an article on bond portfolio immunization against changes in the interest rate. I learned that the immunization can be done against instant changes in interest rate ...
6
votes
1answer
309 views

How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?

I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
3
votes
1answer
232 views

Value of option-free instruments with a short-rate model vs the spot curve

You can calculate the value of an option free bond or swap by using the spot curve and discounting cashflows accordingly. Alternatively, apparently you can use a single-factor short rate model in a ...
6
votes
5answers
1k views

What distribution to assume for interest rates?

I am writing a paper with a case study in financial maths. I need to model an interest rate $(I_n)_{n\geq 0}$ as a sequence of non-negative i.i.d. random variables. Which distribution would you advise ...
5
votes
1answer
288 views

How to value a floor when a loan is callable?

Certain bank loans pay a spread above a floating-rate interest rate (typically LIBOR) subject to a floor. I would like to find the value of this floor to the investor. Assume for this example that ...
7
votes
1answer
675 views

What are the most common/popular exotics in the interest rate markets these days?

By "exotic" I mean anything that is not a plain vanilla swap, swaption, cap or floor. Also any IR hybrids if appropriate. Possible examples would be: CMS and CMS spread options Multi-callable swaps ...
7
votes
1answer
3k views

What is the reason for the convexity adjustment when pricing a constant maturity swap (CMS)?

I'm trying to wrap my head around pricing a Constant Maturity Swap (CMS). Let's imagine the following deal: 6m LIBOR in one direction, 10y swap rate in the other. The discount curve is derived from ...
5
votes
1answer
404 views

What is the forward rate for a Black-Karasinski interest rate model?

I was wondering if anyone could help me with the instantaneous forward rate equation for a Black-Karasinski interest rate model? I was also after the Black-Karasinski Bond Option Pricing Formula.
6
votes
2answers
1k views

Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)?

I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?
6
votes
2answers
1k views

Is Duration really the slope of the Price-Yield curve?

When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve. But is that really right? Duration is (change in price) divided ...
6
votes
1answer
346 views

How to build the short end of a zero coupon curve for non-core Eurozone countries?

I am in the process of building zero coupon curves for some countries in the Eurozone. I have the following data sets: Euribor and EONIA Swap rates Bond price and yields The bond prices (and thus ...
9
votes
1answer
250 views

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

The dominant frequencies for Money Market and FX instruments were 6m and 3m for a long time, and banks slowly moved to commercial trades at those frequencies but funding overnight. If this is a step ...
9
votes
4answers
1k views

Is the risk-free rate really limited by inflation?

In all the classic texts on equities derivatives, there is an assumption of the risk-free rate r. We can immediately dismiss the concept of a fixed rate; all interest rates are variable (and ...
4
votes
1answer
402 views

Is there any gamma in basis (i.e., floating for floating) interest rates swaps?

It is well known that vanilla fixed for floating swaps usually have a bit of gamma, but does a floating for floating (basis) swap have any? For the sake of simplicity, let's assume that both legs of ...
7
votes
1answer
366 views

Do people use unbounded interest rate models, and what alternatives exist?

A simple interest rate model in discrete time is the autoregressive model, $$ I_{n+1} = \alpha I_n+w_n $$ where $\alpha\in [0,1)$ and $w_n\geq 0$ are i.i.d. random variables. When working with ruin ...
5
votes
1answer
172 views

How to scale option pricing components in regard to time

I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model. I have run into a very basic question. How should I scale the input variables in regard to time? My ...
12
votes
6answers
857 views

Setting the r in put-call parity?

Put-call parity is given by $C + Ke^{-r(T-t)} = P + S$. The variables $C$, $P$ and $S$ are directly observable in the market place. $T-t$ follows by the contract specification. The variable $r$ is ...
9
votes
2answers
467 views

When is the LIBOR market model Markovian?

The question is inspired by a short passage on the LMM in Mark Joshi's book. The LMM cannot be truly Markovian in the underlying Brownian motions due to the presence of state-dependent drifts. ...