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Precisely how do you delta-hedge a spot-1Y SOFR IRS with SOFR futures?

I'm struggling to construct hedge ratios that delta-hedge a spot-1Y IRS. Say I'm roughly in the middle of an IMM period, date = Oct 30th 2023 and I trade a 1k dv01 spot-1Y SOFR swap. I'll need some ...
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Convexity adjustment future/fra in practice

The topic of Future/FRA adjustment has already been addressed on a theoretical point view, roughly we need a rate model to calculate the covariance between the money market account of the discount ...
Canardini's user avatar
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3 votes
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179 views

How do I calculate implied convexity from futures vs swaps?

From STIR Futures - Trading Euribor and Eurodollar futures by Stephen Aikin, convexity is determined by comparing the zero rate on a swap with an equivalent set of futures. For example, using futures,...
User27's user avatar
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Derive the convexity adjustment for inflation YoY swap with unconventional payoff

I'm trying to solve for the convexity adjustment for an inflation YoY swap with unconventional payoff, where $I_i$ is CPI at time i: $Notional * ([I_i/I_{i-1}]^{Day Count Fraction} - 1)$ In the normal ...
bphone's user avatar
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1 answer
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Smile Skew and Convexity Exposure

We're all familiar with the Greeks (Delta, Gamma, Vega, etc.). They provide a quantified exposure to various risk factors. But what about skew and convexity? Is there a similar standardized way to ...
Socrates231's user avatar
1 vote
0 answers
104 views

Convexity Adjustment for Average Rate IRS

Suppose that one want to price an Interest Rate Swap with daily averaging, i.e. the floating leg looks like $$Floating~Leg = \sum\limits_{i=1}^N P(T_i)\cdot\frac{\sum_{k=1}^m F(t_k, t_k+\delta)}{m}, ~...
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Zero Coupon Swaps Convexity Adjustments

Can i check here if convexity adjustments are needed for zero coupon swaps?
Benedict's user avatar
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1 answer
321 views

Convexity Adjustments Futures - Sensitivity

If the market prices of SOFR futures are obtained from CME, do we still need to compute convexity adjustments when computing the sensitivity of the IR future?
Benedict's user avatar
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1 vote
2 answers
491 views

SOFR futures options

I am trying to take convexity adjustments into account in the bootstrap on the SOFR curve. I am using cash for the upfront, SOFR swaps from 2Y to the end. In the mid term I use 2 1M SOFR futures and 7 ...
EricFlorentNoube's user avatar
1 vote
0 answers
66 views

Convexity adjustment for inflation

I'd like to prove the following equation: $\mathbb{E}\left[\frac{e^{\int_0^{T_1} y_s d s}}{e^{\int_0^{T_2} r_s d s}}\right]=\frac{\mathbb{E}\left[e^{\int_0^{T_2} r_s d s}\right]}{\mathbb{E}\left[e^{\...
ice_fox21's user avatar
2 votes
2 answers
502 views

Quantifying the impact of rates change on bond prices

How can I quantify the impact of a change in interest rates on bond prices? I know that in a classical textbook setting the answer would be to compute the modified duration of the bond and, to account ...
Peter's user avatar
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221 views

Are there names from the third term onwards in the Taylor approximation for bond pricing?

The first terms are duration and convexity, but are there common names for the terms beyond this?
ltrozzo's user avatar
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1 answer
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Convexity adjustment for futures/FRA under T+D measure

In an internal document in my company, the convexity adjustment for Futures is defined as: where and P(0,T+D) is the ZC bond maturity at T+D. I don't understand why is not equal to 1 as I thought ...
DeltaVanna's user avatar
1 vote
2 answers
477 views

Convexity adjustment doubt

So this the question and the answer to the first one states that only the 5 year swap rate will be adjusted for convexity and the answer to the second one states that neither of the rates will be ...
Pearl Trivedi's user avatar
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0 answers
329 views

Payment Delay Convexity Adjustment Formula for RFR Rates

For Libor we have the following Convexity adjustment formula for payment delay (under normal model) $$CA = P(0,T_e,T_p)\rho\sigma_e^L\sigma_p^L\Delta_e^p(T_s-t_0)$$ where $T_s$ is the period start ...
user62031's user avatar
1 vote
1 answer
236 views

How can I show convexity of this risk function?

I have the following risk function: $\mathbf{Risk}(x):=\mathbb{E}[R(x)]+\delta\mathbb{E}[|R(x)-\mathbb{E}[R(x)]|]$ where $R(x)$ is the portfolio return and $\delta$ is any positive scalar. My textbook ...
L. Johnson's user avatar
4 votes
1 answer
262 views

How am I supposed to understand the following statement on the convexity adjusted rate

Given, a numéraire $(N(t))_{0\leq t \leq T}$ and an index $(X(t))_{0\leq t\leq T}$ that is a $\mathbb Q^{N}$-martingale, we consider the natural payoff $V_{N}(T)$, where it pays $$V_{N}(T):=X(T)N(T) \...
user9078057's user avatar
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1 answer
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Duration and convexity of an open term loan/bond!

Imagine an open term loan with monthly interest payments of [x]% and the principle due when the loan is closed. Both the lender can call the loan, and the borrower can return the loan (with no penalty)...
AnonnonA's user avatar
1 vote
1 answer
630 views

What are the causes of positive convexity in the mortgage market?

In general, mortgage assets are negatively convex. However, I've seen cases of positive convexity and have never seen an adequate explanation for why this might be the case. I suspect it has ...
mortgagequant's user avatar
3 votes
3 answers
992 views

Convexity Adjustment of Daily Compounded Swap under Hull-White Model

I am working on a problem that deals OIS daily compounded swap under Hull-White 1-factor model. I am struggling with pricing the floating leg, on a delayed payment date: $E^{T^p}_t[\prod_{i=0}^{n-1} (...
Fail Analysis's user avatar
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280 views

FX options: is convexity usually heavily overpriced?

I have access to daily vol quotes for EURUSD options from 2006 to today. I was playing around with them and constructed a "daily rolled backtest" for various options constructs, like ...
Volwiz's user avatar
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-1 votes
1 answer
759 views

Question in convex arbitrage [closed]

In convex arbitrage, we say that if the convexity of call(put) price as a function of the strike is violated, we can have arbitrage strategy. For instance, $$ C_{K_2}\geq \lambda C_{K_1}+(1-\lambda) ...
Eulerid's user avatar
1 vote
0 answers
116 views

Influence of Maturity and Yield on Convexity

I recently took a quiz in which one question asked me to choose one answer that is true regarding convexity. One of the answers said that a longer maturity leads to a higher convexity, another answer ...
Maths student G's user avatar
2 votes
1 answer
2k views

RFR boostrapping using RFR OIS: Is convexity adjustment technically necessary?

For single-curve RFR bootstrapping, such as a SOFR-based discounting curve bootstrapped strictly using SOFR fixed-float OIS, I am trying to understand if convexity adjustments are technically ...
subnagus's user avatar
3 votes
2 answers
2k views

Convexity in a DV01 neutral trade

I have got a question about DV01 neutral trades. Generally speaking: if you perform a 2s10s steepener on a generic govt yield curve, would convexity be a risk? If so, in what measures? Technically, as ...
govtbondtrader's user avatar
2 votes
0 answers
105 views

Cost of Volga & Vanna in Credit Options?

What are the commonly used methods to compare the cost of volga/vanna in credit index options across time and strikes? In practice, is the Vanna-Volga exposure technique used in credit, or are there ...
CreditNecromancer's user avatar
-1 votes
1 answer
2k views

QuantLib Python: how to calculate duration and convexity for irregular cashflows? Can I use SimpleCashFlow or must I define a custom bond?

I have 2 questions: If I want to discount a set of irregular cashflows, I can do it using the SimpleCashFlow class, or defining a bond with custom cashflows (thank you to Ballabio and David Duarte for ...
Pythonista anonymous's user avatar
-1 votes
2 answers
82 views

Equations to Test of local linearity of a derivative security [closed]

Friends any hint as to why is this set of equations a test of linearity of a derivative security? From Taleb - Dynamic Hedging pg. 11 ,, Derivatives are not always ...
ExoticBirdsMerchant's user avatar
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1 answer
2k views

Gamma/Convexity of a Swap vs a similar bond

As a rule of thumb, how would the duration and convexity of a 30y UST bond paying X% compare to the duration and convexity of a matched maturity vanilla interest rate swap, with a similar fixed rate. ...
CreditNecromancer's user avatar
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2 answers
274 views

Bond Convexity & Interest Rates [closed]

I am having trouble understanding the convexity of bonds and the relationship among bonds with different convexities. Exactly what is convexity and what is a simple way to For instance, how is it ...
SylvesterAussie's user avatar
1 vote
1 answer
458 views

Duration and Convexity

I am searching to estimate the evolution of my portfolio duration following a yield increase/decrease. Can i use the convexity? I mean IR delta x (- convexity) = Duration delta Is it correct? Thanks a ...
Jerome Zerbib's user avatar
2 votes
0 answers
196 views

Can genetic algorithm help in portfolio optimisation when convexity is not verifiable

I have the following portfolio cost function to maximise: $$ w^T\mu-\frac{1}{2}\gamma w^T\Sigma w+\frac{1}{6}\gamma^2 w^TM_3(w\otimes w), $$ which considers the co-skewness ($M_3$ tensor), $γ$ is the ...
Luigi87's user avatar
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1 vote
1 answer
233 views

How to transform a cubic optimisation problem into a quadratic for portfolio allocation

I have the following cost function for portfolio allocation: $$ w^T\mu-\frac{1}{2}\gamma w^T\Sigma w+\frac{1}{6}\gamma^2 w^TM_3(w\otimes w), $$ which considers also the co-skewness ($M_3$ tensor), $\...
Luigi87's user avatar
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0 answers
512 views

How to calculate the new price of a bond using duration rule and duration with convexity rule?

A bond with a 30 year maturity, par value of $1000 and is 8% p.a. coupon is selling at an yield to maturity of 8% p.a. The modified duration of the the bond at its yield is 11.26%, and its convexity ...
Chandramouli Raman's user avatar
3 votes
3 answers
2k views

Leveraged ETF pair trade, where's the gamma/convexity?

I'm trying to better understand leveraged etfs, and specifically how they have convexity and volatility decay similar to options. An older post on this site asked a similar question and one of the ...
user49866's user avatar
0 votes
2 answers
2k views

Why is portfolio optimization a convex problem if variance is concave?

Variance is concave, so portfolio risk must be too. The mean-variance model employs quadratic programming to optimize (minimize) portfolio risk. My understanding is that quadratic programming requires ...
develarist's user avatar
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0 votes
1 answer
111 views

Convexity of a rates Bermudan w.r.t strike

Recently there was a nice question asked on convexity of American put w.r.t strike: Convexity of an American put option Does the same hold for a Bermudan option in rates, where they underlyings are ...
Arshdeep's user avatar
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1 vote
1 answer
182 views

Is there a way to get convexity adjustements for any CMS-payoffs?

In the litterature we specify a dynamic for $\frac{P(T,T_{p})}{A(T)} = G(S(T))$ for each Swap rate S(T) , and there are supposed independant so that we can obtain some value using copulas for ...
Kupoc's user avatar
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1 answer
280 views

Question About Negative and Positive Convexity

I read the following paragraph from investopedia: https://www.investopedia.com/terms/c/convexity.asp If a bond's duration increases as yields increase, the bond is said to have negative convexity. In ...
M00000001's user avatar
  • 647
6 votes
3 answers
1k views

Convexity of an American put option

Is the price of an American put on an underlying without dividend convex with respect to the strike?
Hans's user avatar
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1 vote
1 answer
143 views

Jensen’s inequality in Convexity adjustment premium

I'm preparing for my FRM II test in May. Could someone help to explain where does the 0.0823 come from? 😥
Betty's user avatar
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2 votes
0 answers
364 views

Are there trades that long gamma (convexity) and short volatility at the same time?

Likewise, are there trades that short gamma and long volatility at the same time? Under fixed income context, are there trades that short convexity and long volatility at the same time?
Harry Lijia Qin's user avatar
2 votes
1 answer
901 views

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-...
M00000001's user avatar
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3 votes
0 answers
841 views

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 ...
Confounded's user avatar
1 vote
2 answers
2k views

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 ...
Peaceful's user avatar
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3 votes
1 answer
363 views

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 $r$ ...
siou0107's user avatar
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1 vote
1 answer
351 views

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 ...
benjbe's user avatar
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3 votes
1 answer
670 views

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 ...
DomingoBrown's user avatar
3 votes
0 answers
56 views

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 ...
guest93456789's user avatar
1 vote
1 answer
366 views

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 ...
blah_crusader's user avatar