Questions tagged [convexity]
The convexity tag has no usage guidance.
111 questions
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Intuition for convexity adjustment for year on year inflation swaps
I am trying to understand the intuition behind why a convexity adjustment is required when calculating the YoY rate on inflation swaps.
(Assume no lags for simplicity). The current inflation index is ...
- 71
0
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1
answer
93
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Bond Option Convexity
As part of my learning, I came across bond convexity and was wondering how that would apply to bond options, as in would it be the expectation of ytm ? How do we define it? Are there any good articles/...
0
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2
answers
111
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Expected future interest rate from FRA or IR futures
I want to know what is expected future rate (fixing, floating rate of fra) in the market. Should i look at the IR futures or FRA rate of the corresponding period? I know they both differ due to ...
0
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0
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43
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Pricing formula for a FX forward with delayed payment
A typical FX forward trade would settle the foreign currency 2 days after the fixing of the FX rate. The forward leg of this trade would be priced by discounting in the domestic currency the value of ...
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0
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1
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156
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Proving that Convexity approx. equals Duration squared but something goes wrong?
I am trying to derive a formula for bond convexity that I saw in a textbook which states that
$$\text{convexity} = \frac{\text{Macaulay duration}^2 + \text{Macaulay duration} + \text{dispersion}}{(1+\...
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1
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1
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49
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How do I reformulate this max GMV ratio constraint in convex way?
Assuming I have N stocks. I want to have the following constraint in my optimization problem setup.
$|x_i| \le \alpha \sum_{j}^N |x_j|$ where $\alpha$ is known, say 0.6. The intuition here is the GMV ...
- 51
0
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0
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57
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Can I add Sharpe Ratio with information ratio in convex way
Sharpe Ratio can be turned into a convex function. And information ratio as well.
Supppose I add these ratios as follows:
(SR + 3 IR ) / 2
Can this function transfer into convex?
How should I do it?
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-3
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1
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173
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sharpe ratio, convert into convex function, not understand that constraint, [duplicate]
I am reading about tranforming sharpe ratio into convex problem
After some following, its converted into min xTxy s.t. (u-rf e)x = 1
...
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2
votes
0
answers
142
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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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0
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281
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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 ...
- 553
3
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0
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298
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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,...
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0
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0
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124
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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 ...
- 1
0
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1
answer
1k
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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 ...
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164
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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}, ~...
- 853
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0
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137
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Zero Coupon Swaps Convexity Adjustments
Can i check here if convexity adjustments are needed for zero coupon swaps?
- 346
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1
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522
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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?
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2
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755
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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 ...
- 271
1
vote
0
answers
91
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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^{\...
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2
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2
answers
697
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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 ...
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2
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279
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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?
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1
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154
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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 ...
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1
vote
3
answers
751
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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 ...
4
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386
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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 ...
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1
vote
1
answer
259
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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 ...
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4
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1
answer
268
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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
$$V_{N}(T):=X(T)N(T) \...
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1
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95
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Duration and convexity of an open term loan/bond!
Imagine an open term loan with monthly interest payments of [x]% and the principle due when the loan is closed. Both the lender can call the loan, and the borrower can return the loan (with no penalty)...
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1
vote
1
answer
813
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What are the causes of positive convexity in the mortgage market?
In general, mortgage assets are negatively convex. However, I've seen cases of positive convexity and have never seen an adequate explanation for why this might be the case. I suspect it has ...
3
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3
answers
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Convexity Adjustment of Daily Compounded Swap under Hull-White Model
I am working on a problem that deals OIS daily compounded swap under Hull-White 1-factor model. I am struggling with pricing the floating leg, on a delayed payment date:
$E^{T^p}_t[\prod_{i=0}^{n-1} (...
0
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0
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387
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FX options: is convexity usually heavily overpriced?
I have access to daily vol quotes for EURUSD options from 2006 to today. I was playing around with them and constructed a "daily rolled backtest" for various options constructs, like ...
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1
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887
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Question in convex arbitrage [closed]
In convex arbitrage, we say that if the convexity of call(put) price as a function of the strike is violated, we can have arbitrage strategy. For instance,
$$
C_{K_2}\geq \lambda C_{K_1}+(1-\lambda) ...
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vote
0
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135
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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 ...
2
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1
answer
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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 ...
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3
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2
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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 ...
2
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0
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113
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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 ...
-1
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1
answer
2k
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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 ...
-1
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2
answers
84
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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 ...
0
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1
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2k
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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.
...
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2
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337
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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 ...
1
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1
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564
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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 ...
2
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0
answers
201
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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 ...
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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), $\...
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593
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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 ...
3
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3
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2k
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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 ...
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2
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2k
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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 ...
- 3,090
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1
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131
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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 ...
- 2,561
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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 ...
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314
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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 ...
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3
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Convexity of an American put option
Is the price of an American put on an underlying without dividend convex with respect to the strike?
- 2,876
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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? 😥
- 171
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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?
