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1

Smile arbitrage is the presence of a butterfly spread arbitrage in a given maturity of your surface, i.e. if your call prices are non-convex leading to an arbitrage. An easy way to spot the arbitrage is to build the call prices and check for strictly convex prices in strike. If you have a parametrisation of the implied volatility $\sigma(K)$ then you can ...


5

I answer from a general discrete time/discrete state model point of view. This includes the binomial tree model as a special case. In finite dimensions, you can interpret asset payoffs and returns as vectors and retreat to linear algebra. Suppose you have $N$ states of nature and $J$ assets. Your payoff matrix is \begin{align*} A=\begin{pmatrix} X_1(\omega_1)...


3

as it was stated correctly in the question all long butterfly options have to have a non-negative premium in order for No-arbitrage to hold. So we can say that: No-Arbitrage holds implies All Butterfly spreads have a non-negative premium. However, the reverse is not true. Just because all butterfly spreads have non-negative premiums does not mean that ...


2

It sounds like you haven't filtered away static arbitrage strategies (such as butterfly spreads, call spreads and calendar spreads) from your data. To keep my answer short and concise, there's a paper by Carr & Madan (2005) that establish the structure of a finite set of tests (a filtering procedure) on your option quotes. When you are left with options ...


4

I am not sure why the question you link to does not provide an answer. I’ll try to answer it but it is really similar to what has already been said there. Bottom line is: if the value $K$ is reachable by the underlying asset $S$, that is $K$ belongs to the domain of process $S$, then the butterfly should be strictly positive. First note that the butterfly is ...


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