Questions tagged [convexity]

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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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3 votes
1 answer
316 views

What is gamma to do with realized volatility?

I keep hearing that gamma is a bet on realized volatility. That is, if we are long gamma then we need higher realized volatility to come in the future in order to make a profit. from other source: If ...
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Portfolio optimization - Correlation risk stress testing - DCP

I have a script based on Python/CVXPY trying to define the portfolio with the maximum expected return, given some risk constraints. I would like to introduce a constraint that limits correlation risk. ...
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0 answers
112 views

Why is the Sortino ratio non convex and also non concave?

I am considering as my objective the Sortino ratio: $\frac{\mu^{\top}x-R}{\sqrt{\mathbb{E}[(min\{0,(r-\mu)^{\top}x\})^2]}}$ In my textbook they state that this ratio just like the Sharpe ratio is ...
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1 vote
1 answer
141 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 ...
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4 votes
1 answer
242 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) \...
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0 votes
1 answer
66 views

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
128 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 ...
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3 votes
3 answers
402 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} (...
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101 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 ...
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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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1 vote
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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 ...
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2 votes
1 answer
536 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 ...
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2 votes
2 answers
685 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 ...
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2 votes
0 answers
75 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 ...
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-1 votes
1 answer
698 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 ...
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-1 votes
2 answers
69 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 ...
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1 answer
556 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. ...
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2 answers
118 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 ...
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1 vote
1 answer
189 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 ...
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2 votes
0 answers
178 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 ...
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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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223 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 ...
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3 votes
3 answers
862 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 ...
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0 votes
2 answers
921 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 ...
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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 ...
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1 vote
1 answer
99 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 ...
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1 answer
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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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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?
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1 vote
1 answer
89 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? 😥
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2 votes
0 answers
217 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?
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2 votes
1 answer
606 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-...
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1 vote
0 answers
556 views

OIS curve convexity adjustment

Since, as far as I understand, an Overnight Index Rate is a 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 be ...
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2 votes
2 answers
1k 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 ...
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3 votes
1 answer
264 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 $r$ ...
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1 vote
1 answer
256 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 ...
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3 votes
1 answer
178 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 ...
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3 votes
0 answers
49 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 ...
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1 vote
1 answer
195 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 ...
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2 votes
1 answer
1k views

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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2 votes
2 answers
3k views

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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2 votes
0 answers
100 views

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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3 votes
1 answer
293 views

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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7 votes
3 answers
2k 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 ...
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0 votes
1 answer
228 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. ...
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3 votes
2 answers
365 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 $E_Y(P_Y)$, ...
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1 vote
2 answers
891 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 ...
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1 vote
1 answer
623 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?
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  • 177
1 vote
1 answer
440 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 ...
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3 votes
0 answers
42 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 ...
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