Skip to main content
12 votes
Accepted

Why are FRA/futures convexity adjustments necessary?

This has been posted a few times now, so I will invest the time on a full response. FRA / Futures convexity has nothing to do with profits/losses being immediately recognised on the future through ...
Attack68's user avatar
  • 10.8k
12 votes

Convexity of an American put option

It is indeed. The price of an American option is the Bermuda option in the limit that the exercising interval approaches zero. The Bermuda option at any exercising time can be evaluated inductively ...
Hans's user avatar
  • 2,806
10 votes

Why is there a convexity adjustment if the payment date differs from Libor end date?

Let us denote $\delta$, the Libor's tenor (e.g. 3M), $P(t, T)$ the price of a zero coupon bond price paying 1 unit of currency at $T$, and $L_t(T, T + \delta)$ the forward 3M Libor starting at $T$ and ...
byouness's user avatar
  • 2,230
9 votes
Accepted

Convexity of an American put option

Here is a much more straightforward proof of the convexity of the American option with respect to a parameter, if it is independent of time and deterministic, than my previous one, though I am happy ...
Hans's user avatar
  • 2,806
7 votes

What is the correct convexity adjustment for an Interest Rate Swap with unnatural reset lag?

Consider a date sequence \begin{align*} 0 \leq t_0 \leq T_s < T_p < T_e, \end{align*} where $t_0$ is the valuation date, $T_s$ is the Libor start date, $T_p$ is the payment date, and $T_e$ is ...
Gordon's user avatar
  • 21.2k
7 votes

Convexity in a DV01 neutral trade

Let’s say you do a 2s-10s steepener, dv01 neutral. What does this mean ? It means you are using the current dv01s of the 2s and 10s, which are approximately 1.99 and 9.12, to weight the relative ...
dm63's user avatar
  • 17.2k
6 votes
Accepted

A very simple question about convexity of a bond

The chart you posted does not give a correct visual representaion of convexity . Convexity is not $\frac{\partial^2 P}{\partial y^2}$ but $\frac{1}{P}\frac{\partial^2 P}{\partial y^2}$. So you have to ...
nbbo2's user avatar
  • 11.5k
6 votes
Accepted

B-splines: convexity in IV/Price

No, and this is wrong. The implied vols (from market prices) are actually not necessarily convex but yet may be still arbitrage-free, there are many examples of this for various equities. Furthermore, ...
jherek's user avatar
  • 1,414
5 votes

Can two bonds have same yield and price but different convexity?

To directly answer the question: bond A= one day to maturity , price 100, yield 2%. Bond B: 10 years to maturity, price 100 yield 2%. This is perfectly possible. Bond B has greAter convexity but ...
dm63's user avatar
  • 17.2k
5 votes

Why is there a convexity adjustment if the payment date differs from Libor end date?

Consider a date sequence \begin{align*} 0 \leq t_0 \leq T_s < T_e < T_p, \end{align*} where $t_0$ is the valuation date, $T_s$ is the Libor start date, $T_e$ is the Libor end date, and $T_p$ is ...
Gordon's user avatar
  • 21.2k
5 votes

Convexity of an American put option

Let $\mathscr{T}$ be the set of stopping times with values in $[0, T]$. Note that, for any $\tau \in \mathscr{T}$, $\lambda_1\ge 0$, $\lambda_2 \ge 0$, and $\lambda_1+\lambda_2 =1$, \begin{align*} &...
Gordon's user avatar
  • 21.2k
4 votes
Accepted

Proof of the convexity adjustment formula

Well, you need to know what is the stochashtic model you are using for $y_T$, if you assume it's a geometric brownian motion you have this process : $y_T = y_0 e^{\sigma W_T - \frac{1}{2} \sigma^2T} $...
user30150's user avatar
4 votes
Accepted

Interest Rate Convexity - Fundamental Question

This is indeed just a convention, as you point out. It comes from the fact that zero coupon bonds, by convention, do not have any volatility exposure. Rather, it is assumed the prices of ZCBs are ...
dm63's user avatar
  • 17.2k
4 votes
Accepted

How to Take Advantage of Arbitrage Opportunity of Two Options

I think it is far easier to understand by just drawing the payoffs. You have two put options: A European put option on a non-dividend paying stock with strike price 80 is priced at 8 dollars, and a ...
Magic is in the chain's user avatar
3 votes
Accepted

SPX Convexity Spread

You can think of both ( difference and ratio ) indicators as some aggregated measure of difference between flat vol (ATM vol) and "total vol" than includes skew and kurtosis effects.
onlyvix.blogspot.com's user avatar
3 votes
Accepted

Derivation of convexity formula

You have left out the chain rule term in the first derivative and second derivative. First derivative should be: $$\frac{\partial P}{\partial YTM} = \frac{1}{2(1+YTM/2)} \sum_{i=1}^N \frac{-2 t_i ...
gdlamp's user avatar
  • 196
3 votes

High convexity vs low convexity bond definition

Do not forget the effect of passing time (the theta) on your portfolio. If two portfolios have the same value and duration, then the portfolio made up of the difference has locally zero sensitivity ...
Antoine Conze's user avatar
3 votes

Change of numeraire from bank account to Zcb

Let $B_t= e^{\int_0^t r_sds}$ be the money-market account value at time $t$, and $P(t, T)$ be the value of the zero-coupon bond with maturity $T$ and unit face amount. Moreover, let $Q$ be the risk-...
Gordon's user avatar
  • 21.2k
3 votes

Curve steepner and convexity

If you know what convexity is then you will know that products with longer maturity have higher convexity, e.g. swaps and bonds. Convexity (gamma) is also generally quadratic so increases faster than ...
Attack68's user avatar
  • 10.8k
3 votes

What is the correct convexity adjustment for an Interest Rate Swap with unnatural reset lag?

This seems to be a (short term, only 3 months) CMS swap. I wrote a paper about the different approaches to price them, available here. You can pick the one best fitted for your needs.
Sithered's user avatar
  • 808
3 votes

Interest Rate Convexity - Fundamental Question

OK, so I think I have this figured out in my head now in terms of martingale measure theory. Thanks dm63 for pointing me in the right direction! Just for my own peace of mind and perhaps to help ...
Kotov's user avatar
  • 93
3 votes

Why is there a convexity adjustment if the payment date differs from Libor end date?

The other two answers do a good job of explaining, within the context of mathematical financial models, why a convexity adjustment is necessary, but I think a more tangible perspective can also be ...
Chris Taylor's user avatar
  • 5,931
3 votes
Accepted

Jensen’s inequality in Convexity adjustment premium

$P_2-P_1$ where: $P_1=\frac{1000}{\left(1+\frac{0.06+0.04}{2} \right)\left(1+0.05 \right)}$ $P_2=0.5\frac{1000}{\left(1+0.06 \right)\left(1+0.05 \right)}+0.5 \frac{1000}{\left(1+0.04 \right)\left(1+...
Magic is in the chain's user avatar
3 votes

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

I'm in no way a portfolio theory expert, but the negative of a convex function is concave and vice versa. You can look at minimizing a concave function as maximizing a convex function and vice versa. ...
Arshdeep's user avatar
  • 2,451
3 votes

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

Both products actually have positive convexity, they will buy more underlying (SP500) when the price goes up and sell it when it goes down. However, if you hedge every day, you will just cancel out ...
Lliane's user avatar
  • 2,908
3 votes

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

I disagree that these products are convex*. At any point in time, the ETF exposure to the underlying is linear, it's just that it changes through time. A 2x ETF will just have 2x exposure to the ...
will's user avatar
  • 2,581
3 votes

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

As @Lliane explains, you are actually describing a position in which the underlying is rebalanced everyday, hence the compounding effect of the leveraged ETF vanishes. Maybe a bit of modelling can be ...
Daneel Olivaw's user avatar
3 votes

Bond Convexity & Interest Rates

Assume we are using continuously compounding rates, and that discount factors are given by the ZCBs $P(0, t_i) = e^{-y_i \cdot t_i}$. The price of a fixed bond is given by $$B = \sum_1^n N \cdot \...
Pontus Hultkrantz's user avatar
3 votes
Accepted

Question in convex arbitrage

See the graph below. Let's define the PNL as the position's payoff at expiry plus accrued initial investment, i.e. collected / paid option premia. Assuming $K_1=95,K_2=100,K_3=105$ (i.e. $\lambda=0.5$)...
Kermittfrog's user avatar
  • 6,822
2 votes

What is the correct convexity adjustment for an Interest Rate Swap with unnatural reset lag?

What you need is the convexity adjustment for 3 month libor when the payment is made 1 month after the reset date (ie 2 months before the natural date). As an approximation, this will be ...
dm63's user avatar
  • 17.2k

Only top scored, non community-wiki answers of a minimum length are eligible