Questions tagged [convexity]
The convexity tag has no usage guidance.
111 questions
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How to Take Advantage of Arbitrage Opportunity of Two Options
I got the following interview question and corresponding solution, but I have a different understand that might be wrong, so I really appreciate your advice on it:
A European put option on a non-...
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OIS curve convexity adjustment
Since, as far as I understand, an Overnight Index Rate is set in arrears, i.e. it is published in the morning after the night to which the rate applies, then I would have thought that we should take ...
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convexity adjustment for pricing mark to market (mtm) cross currency swap
may I know where the convexity adjustment is from and in practice, how is it usually calculated?
is it coming from the correlation between fx and rates ?
am I right that non-mtm cross currency swap ...
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Forward price vs. futures price - Wilmott
I am reading Paul Wilmott's book PWOQF2, and there is something I don't get in his derivation of the convexity adjustment between forward and futures prices (chap. 30).
He models $S$ and $r$ ...
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Estimation of LIBOR 3M periods if the period is not exactly 3M months
When generating dates of interest rate swaps, even without stub periods, we sometimes end up with periods that are less than 3 months (say 87 day). In that case do we have to apply any kind of ...
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B-splines: convexity in IV/Price
I see that the justification of the need to use cubic B-splines when interpolating in the strike-IV space is to impose a convexity constraint to get rid of potential arbitrage.
I could easily ...
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Does convexity in the IV space means convexity in the price space?
Let's assume that we only look at OTM options to construct a Risk Neutral Density (RND).
As the RND is the second derivative of the price of the option with respect to the strike, we would expect ...
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Hedging convexity for long-dated fixed cashflows
I'm wondering what are the different ways of hedging the convexity in fixed long-dated cashflows (maturity > last liquid point). Also, if you'd say receiver swaptions would be the way to go, could you ...
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Price Alignment Interest(PAI) Convexity Effect
I've been looking at convexity adjustments in ED's for several years(more opportunities a few years ago then currently) and was wondering if my thinking on PAI impact on swaps convexity is correct.
...
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Why are FRA/futures convexity adjustments necessary?
This would be my explanation for the reason that convexity adjustments must exist:
Futures are margined daily, such that if a trader is paid a future and rates goes up then money is paid into their ...
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Convexity Adjustment on sensitivity computation for Futures
Convexity adjustment is a correction term that helps in deriving futures price from forward price and vice versa. But, will this convexity adjustment come into play when we are trying to compute ...
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MBS Market Duration & Convexity
Soft question...hopefully.
I am working on a swaption hedging strategy. Part of this strategy calls for a forward looking indication of changes in implied volatility, using 1m10y implied as a proxy ...
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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 ...
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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. ...
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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 $E_Y(P_Y)$, ...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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}...
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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 ...
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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:
"...
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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 ...
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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^{-\...
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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 ...
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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 ...
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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)^{...
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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 ...
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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) ?
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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 ...
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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 ...
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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 ...
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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 ...
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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 rather than ...
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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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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 ...
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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?
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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: ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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'...
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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 = ...
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