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Questions tagged [convexity]

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7
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3answers
158 views

Why is there a convexity adjustment if the payment date differs from Libor end date?

A 3 month LIBOR that fixing at $T$, paying in 3 months does not have a convexity adjustment. However, 3 month LIBOR fixing at $T$, paying in 6 months needs a convexity adjustment. How is this shown ...
0
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1answer
55 views

Convexity adjustment--Assume sport and futures rates move together?

A cash flow argument I typically see for why a convexity adjustment is necessary is the following (taken loosely from Hull 9/e, p. 143): Say I am short an interest rate futures contract (e.g. ...
3
votes
2answers
96 views

Why isn't a quanto adjustment needed in this case?

Suppose we have a contract with payoff $P_Y$ in currency $Y$, where $P_Y$ on a variable in currency $Y$. To calculate the value in $X$, we take the expected payout under $Y$-numeraire $E_Y(P_Y)$, ...
1
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2answers
91 views

Can two bonds have same yield and price but different convexity?

In the market, if there are two bonds that have the same yield and price, then the higher convexity bonds will be more attractive. However, this would mean the market would increase the price of the ...
0
votes
1answer
103 views

Curve steepner and convexity

Can someone please explain why a curve steepener trade has a negative convexity? And are the gains from the steepness of the curve offset by the negative convexity?
1
vote
1answer
91 views

20s30s curve convexity

Let’s assume I trade a 20s30s spread on the curve and i’m flat delta (-100k on 20Y swap, 100k on 30y swap dv01). If the market moves, i’m not flat delta anymore. Is there a simple way to estimate the ...
2
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0answers
28 views

Utility Maximization on a finite Probability Space. Possible mistakes in a paper?

I am currently reading this paper on utility maximization in a financial market model. On page 5 the author starts with the case of a finite probability space and on page 19 he considers the ...
1
vote
1answer
74 views

SPX Convexity Spread

In this report on volatility from BNP Paribas, https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true it states on Page 10 that the SPX ...
0
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2answers
105 views

Bond Convexity and Maturity

What the reasoning for why bond convexity increases with maturity. Heuristic explanations are somewhat better as I would like a fundamental understanding. Also what causes a more convex bond to be ...
0
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1answer
58 views

Which volatility input for in-arrear convexity correction?

When pricing a Libor-in-arrear swap, I am using the following formula (for the cashflow covering the period $[T_{i-1}, T_i]$, ie. paid at $T_i$ and resetting at $T_i$): $V(t) = P(t,T_i)F(t;T_i,T_{i+1}...
1
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1answer
629 views

High convexity vs low convexity bond definition

Isn't high convexity always better than low convexity bond from the formula that $$\frac {ΔB} B=-D \frac {Δy} {1+y} + \frac 1 2 CΔy^2$$ Since $\frac 1 2 CΔy^2$ is positive no matter what so the price ...
1
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1answer
268 views

Empirical duration and convexity for bonds using linear regression

I have a given time series of bond yields from Quandl. From the time series, I have taken a sample to simulate a path of bond yields by Monte Carlo in Python. I have to do the following task: "...
2
votes
1answer
119 views

Convexity adjustment when payment if after interest natural term?

I've been working with a convexity adjustment for an interest rate payoff and the next question came to me: The usual problem that gives rise to the convexity adjustment I'm referring to is as ...
2
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0answers
59 views

How to calculate the product of forward rates with different reset times using Ito's lemma?

I am curious about a calculation I saw in this question. Specifically in this equation: \begin{align*} &\ L(T_s, T_p, T_e) L(T_s, T_s, T_e) \\ =&\ L(t_0, T_p, T_e) L(t_0, T_s, T_e) e^{-\...
2
votes
1answer
483 views

The relation between coupon and convexity

Here are three statements: A lower coupon bond exhibits higher duration. The higher the coupon rate, the lower a bond’s convexity. Zero-coupon bonds have the highest convexity. Given particular ...
2
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0answers
222 views

Modified duration and convexity of a bond in R

A soft question: Are there any existing packages in R that allows one to compute the modified duration and convexity of bonds in R? If there isn't, how can one go about doing so (with formulas) with ...
1
vote
1answer
437 views

Derivation of convexity formula

Let's say that I have a bond that pays coupon on a semi-annual basis. Therefore, the price of this bond can be calculated using the following formula: $$ P = \sum_{i=1}^N \frac{CF_i}{(1 + YTM/2)^{...
0
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1answer
140 views

Convexity for historical bond data

I'm trying to write a program to calculate the convexity of a bond. The bigger idea is, that if I have access to the actual price for each point in time, I should be able to calculate various features ...
0
votes
1answer
230 views

Change of numeraire from bank account to Zcb [closed]

Why is there no drift adjustment when numeraire is changed from bank account (risk neutral measure) to zero coupon bond who matures at time of payoff (fwd risk neutral measure) ?
0
votes
1answer
208 views

A very simple question about convexity of a bond

I was always under the impression that, ceteris paribus, higher the coupon rate, higher the convexity of the bond. But Investopedia says the following: "zero-coupon bonds have the highest degree ...
4
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2answers
174 views

Active share portfolio constraint

I was reading a paper from Cremers and Petajisto, called How Active is Your Fund Manager? A New Measure That Predicts Performance In the original paper from 2009 they have the following measure ...
1
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1answer
379 views

convexity adjustment in YOY inflation swap , compared with TRS, and considering autocorrelation

a YOY inflation swaplet payoff is S2/S1 - 1 , where Si is the CPI at time i and a TRS (total return swaplet) asset leg payoff is also the same except the underlying is an asset. So it seems to me ...
-1
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1answer
253 views

CMS convexity adjustment in a range accrual Monte Carlo

I'm trying to price a CMS indexed range accrual using Monte Carlo simulations. Let's say i have n trajectories of ZC rates using G2++ model under risk neutral measure. My question is how do i take ...
1
vote
1answer
89 views

Hedging equities portfolios with vol products

Quote Hedging with variance is not comparable to puts Due to the lack of convexity of a variance swap hedge, we believe it is best to compare long variance hedges to hedging with futures ...
1
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1answer
330 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 ...
0
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1answer
375 views

Basis swap spread pricing and bootstrapping

Here is the expression of a basis floating versus floating swap where the first term is a forward CMS Swap leg and the second one is a forward BOR leg where X is the margin that would make equal both ...
0
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2answers
410 views

Bond Duration hedging with long convexity

How do you build a duration-neutral bond portfolio which is long convexity? can you give me an example?
7
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3answers
1k views

What is the correct convexity adjustment for an Interest Rate Swap with unnatural reset lag?

I am looking at the valuation of an Interest Rate Swap (IRS thereafter) which is pretty much vanilla with one small tweak. Floating leg pays 3 months LIBOR in monthly intervals. To be precise: ...
1
vote
1answer
581 views

Proof of the convexity adjustment formula

Let $y_0$ be the forward bond yield observed today for a forward contract with maturity $T$, $y_T$ be the bond yield at time $T$, $B_T$ be the price of the bond at time $T$ and let $\sigma_y$ be the ...
5
votes
1answer
2k views

Why does a barbell portfolio have higher convexity than a bullet porfolio

I cannot quite understood absolutely why a barbell portfolio has higher convexity than a bullet porfolio. I can easily understand how the parallel line represents duration but I cannot see what the ...
-2
votes
2answers
503 views

Why Is Bond Time Value Risk Not Considered in Bond Immunization?

I know bond portfolio immunization includes duration and (if the hedging period is longer) convexity matching. These are equivalent to taking the first and second partial derivatives of the bond ...
6
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3answers
1k views

Interest Rate Convexity - Fundamental Question

I have a very basic question around convexity adjustments in swap valuations. I am comfortable with the mathematical derivation of the convexity adjustment. My question relates to when and why a ...
0
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1answer
418 views

long fra and a short ed future with same fixing dates, is convexivity negative or positive?

If you are long a FRA (forward rate agreement) and short a ED (Eurodollars) future with the same fixing dates, do you have positive convexity or negative convexity? Why? According to the following ...
2
votes
1answer
166 views

Pricing function $P(S,t)$ is convex in $S$ for all $t$

I am now reading Alternative Characterization of American Put Options by Carr et all (available at http://www.math.nyu.edu/research/carrp/papers/pdf/amerput7.pdf). There is a theorem called 'Main ...
0
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1answer
499 views

Convex risk measure and a coherent risk measure?

A coherent risk measure is: $\rho(\lambda X_1+(1-\lambda X_2))$ How can it be shown that everey convex risk measure is indeed a coherent risk measure? I assume that it is enough to show that a ...
0
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2answers
203 views

Duration vs. Convexity Contradiction

A lower coupon bond exhibits higher duration, which means higher price volatility with changing YTM. A lower coupon bond also exhibits higher convexity. However, with higher convexity, bond prices ...
3
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1answer
125 views

How to calculate $E^{T_N}(L(T_i, T_{i+1}))$?

suppose $L(T_i, T_{i+1})$ is the LIBOR rate between $T_i$ and $T_{i+1}$, and $T_N$ is some time later than $T_{i+1}$. $E^{T_N}$ is the $T_N$-forward measure. I tried to work this out using John Hull'...
6
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1answer
1k views

Sharpe Maximization under Quadratic Constraints

When doing Sharpe optimization $$ \max_x \frac{\mu^T x}{\sqrt{x^T Q x}} $$ there is a common trick (section 5.2) used to put the problem in convex form. You add a variable $\kappa$ such that $x = ...
4
votes
2answers
120 views

When would dedicated portfolios do better than 'immunized' portfolios?

We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said: It should be ...
2
votes
1answer
129 views

Quick way to extrapolate call price as function of strike

Let's say I know the price of a call for two different values of strike. Is there a quick way to guess the price for another value of strike ? Actually, I know that C(100)=15 and C(90)=20 and I have ...
1
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0answers
72 views

Pricing inflation lags

I've been looking into a short piece of maths I found on pricing inflation with payment delays, and was hoping someone could confirm whether my understanding was correct or if the maths isn't quite ...
4
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0answers
114 views

Inflation/Rates Correlation

I've been looking into a short piece of maths a colleague has written on pricing inflation with payment delays, and was hoping someone could confirm whether my understanding is correct, or if my ...
4
votes
2answers
387 views

How does this follow from the separating hyperplane theorem?

This is from Pliskas book in mathematical finance. I do not know what was best to write the question so I included the pages from the book. He has not written what form of the separating hyperplane ...
3
votes
1answer
301 views

Girsanov theorem in CMS convexity derivation

I am going through the derivation of CMS convexity from the notes of Lesniewski There is a transformation from $T_p$ forward measure to annuity measure $Q$ as $$ P(0,T_p)E^{Q_{T_p}}\left[S(T_0,T)\...
0
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0answers
632 views

Convexity of Portfolio Containing Eurodollar Future and Forward Rate Agreement

Assume an individual is a buyer, i.e., long, of one Forward Rate Agreement and a seller, i.e., short, of one Eurodollar Futures contract. Does the collective portfolio have positive or negative ...
3
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1answer
168 views

What's the underlying idea of definition of constrained market in Skiadas' Asset Pricing Theory?

I'm self-studying Skiadas' Asset Pricing Theory, and find the definition of constrained market on page 21 confusing(you can find it here in the sample chapter). Definition 1.26. A constrained market ...
7
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1answer
813 views

Bond Convexity Treasuries Futures

I know long duration bonds, on a a single bond basis, exhibit convexity however do treasury futures prices and the 10 yr yield exhibit the same property? Below is a plot of continious ten year ...
7
votes
5answers
17k views

Convexity adjustment for a forward swap rate

I recently heard that for a forward swap rate (for example, the fixed rate of a swap that will start in one year and end in five years), I need to do a convexity adjustment in order to get the right ...
2
votes
1answer
209 views

Do taking in account the CSA create convexity effects in your stripping?

When you strip your rate curves using CSA, what kind of convexity effects might appear as a result when computing the CSAed curve from one fixing to another ? For example if you are valuing an USD ...