# Tag Info

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For a 3D graph, your data can only have two independent dimensions. In case of option prices, its probably the strike or moneyness on one axis and the time to maturity on the other. The third axis is for the values to be plotted; in your case that would be the error values. I think what you are looking for is the surf function. Assuming error is a matrix ...

6

To recover the Black-Scholes pricing equation, you should first express the standard normal cdf in terms of its characteristic function analogous to the Heston solution: $$N(x) = \frac{1}{2} - \frac{1}{\pi} \int_0^{\infty} Re [\frac{e^{-i\phi x} f(\phi)}{i\phi}] d\phi$$ where $f(\phi)$ is the characteristic function of the standard normal distribution:  ...

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Levy's Arcsine Law for Brownian motion is quite paradoxical. If you should guess the amount of time a Brownian path spends above or below zero, which percentage of time would you intuitivly assume to be the most probable? I would have guessed 50:50 above and below should be the most probable case. This is wrong and Levy's Arcsine Law explains the correct ...

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Yes, Black Scholes breaks down absolutely for real market conditions at deep in the monies. Please remember that this isn't my specialty, so I can only give my observations. The reason to me seems that only variance can be specified because BS assumes lognormality. Prices certainly aren't lognormally distributed. The best fit I've found is logVariance ...

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Most likely you are looking at bid prices which are lower that fair (theoretical) price. It is very common that bid price of an ITM option is below the lower bound as bid-ask spreads are wide. The IV of ITM call at theoretical price should match IV of OTM put at corresponding strike. If this does not happen then check your forward price, rates and dividends. ...

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The lower bound is not just a BS-specific bound. It is a no-arbitrage bound and so if the price is lower than this, you have an arbitrage opportunity (some good explanation here). It doesn't mean it is present in the market necessarily, because mid price is not necessarily the price you can trade and when you take spread into account this is likely to go ...

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