# Tag Info

## Hot answers tagged convexity

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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*} &...
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### 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 : $y_T = y_0 e^{\sigma W_T - \frac{1}{2} \sigma^2T}$...
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### 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 ...
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### 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 ...
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### 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.
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### 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. $\lambda=0.5$)...
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