# Questions tagged [convexity]

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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: ...
20k 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 ...
926 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 ...
641 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 ...
2k 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 ...
2k views

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 $x = ... 1answer 3k views ### Why does a barbell portfolio have higher convexity than a bullet porfolio I cannot quite understood absolutely why a barbell portfolio has higher convexity than a bullet porfolio. I can easily understand how the parallel line represents duration but I cannot see what the ... 2answers 220 views ### Active share portfolio constraint I was reading a paper from Cremers and Petajisto, called How Active is Your Fund Manager? A New Measure That Predicts Performance In the original paper from 2009 they have the following measure ... 2answers 127 views ### When would dedicated portfolios do better than 'immunized' portfolios? We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said: It should be ... 2answers 446 views ### How does this follow from the separating hyperplane theorem? This is from Pliskas book in mathematical finance. I do not know what was best to write the question so I included the pages from the book. He has not written what form of the separating hyperplane ... 0answers 135 views ### Inflation/Rates Correlation I've been looking into a short piece of maths a colleague has written on pricing inflation with payment delays, and was hoping someone could confirm whether my understanding is correct, or if my ... 2answers 148 views ### Why isn't a quanto adjustment needed in this case? Suppose we have a contract with payoff$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)$, ... 1answer 338 views ### Girsanov theorem in CMS convexity derivation I am going through the derivation of CMS convexity from the notes of Lesniewski There is a transformation from$T_p$forward measure to annuity measure$Qas P(0,T_p)E^{Q_{T_p}}\left[S(T_0,T)\... 1answer 169 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 ... 1answer 148 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 ... 1answer 127 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'... 0answers 39 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 ... 0answers 33 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 ... 1answer 222 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 ... 1answer 266 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-... 1answer 70 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 ... 2answers 148 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 ... 1answer 227 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. ... 1answer 134 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 ... 1answer 244 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 ... 1answer 857 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 ... 1answer 258 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 ... 0answers 51 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 ... 0answers 70 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^{-\... 0answers 368 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 ... 2answers 365 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 ... 2answers 212 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 ... 1answer 110 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 ... 1answer 857 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 ... 1answer 235 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? 1answer 971 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$$Since \frac 1 2 CΔy^2 is positive no matter what so the price ... 1answer 530 views ### Empirical duration and convexity for bonds using linear regression I have a given time series of bond yields from Quandl. From the time series, I have taken a sample to simulate a path of bond yields by Monte Carlo in Python. I have to do the following task: "... 1answer 878 views ### Derivation of convexity formula Let's say that I have a bond that pays coupon on a semi-annual basis. Therefore, the price of this bond can be calculated using the following formula:$$ P = \sum_{i=1}^N \frac{CF_i}{(1 + YTM/2)^{... 1answer 544 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 ... 1answer 104 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 ... 1answer 76 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 ... 1answer 179 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 ... 1answer 476 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: $$ForwardRate = FuturesRate - \frac{1}{2}\sigma^2T_1T_2$$ whereT_1\$ refers ...
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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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### 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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### 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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### 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 ...
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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 ...