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If the security has negative correlation with other assets that enjoy attractive risk-free rates, then it can be attractive at a return rate under the risk-free level. It would, of course, never be a …

First, note that there are actually quite a few implied volatility curves...I am afraid there is no "the" volatility curve. Right off the bat I can think of The put and call bid and offer curves Th …

If you think it is too computationally intensive, you are probably not using enough numerical analytic "tricks", such as control variates. Using them, you will generally find american option pricing …

It's extremely common in the industry to have a parabolic skew of this type with some cutoff parameters. At it's simplest, such a model looks like this $$ \sigma_{ATM}(t) = \sigma_0 + s(t) $$ where …

Implied volatility represents the market expectation of "stuff happening in the future". Over long periods, all that stuff tends to cancel out a bit, so long-term vols are much more stable. In the s …

No, there is an upper limit to a binary option's value, based on the interest rate and how much of the distribution can be packed under the payoff region. Essentially $$C = e^{-rT} \int_K^\infty \p …

This is a problem commonly faced by investment banks and buy-side firms (such as hedge funds) that deal in lots of derivatives. There isn't much more one can do than employ a few rules of thumb, and t …

If you can get anywhere close to the same open-interest and volume using European options as the corresponding American ones, you'll have a much easier time just using them. American options with hig …

The skew alone is not enough. You can see this by noting the one-to-one correspondence between volatility skew and terminal probability distributions, which is independent of price and volatility dyn …

Consider a more financially plausible model than Black-Scholes: one where the stock can suddenly go bankrupt due to fraud, and the volatility varies over time. Neither model is perfect, but the new o …

You can see concavity in mean-reverting underlying assets where the option tenor is comparable to the characteristic reversion time of the asset. For a geometric brownian motion, all underlying price …

Generally, you should ignore deep in-the-money option prices because they are far less liquid (due to their low leverage). That lets you use just the calls on the high strikes and just the puts on th …

In fact, even your VIX dynamics are not exact, since you can only obtain dynamics for an approximation of the actual VIX calculation (I presume you are just running the variance variable through a squ …

The focus on volatility comes about because all price changes "look like" volatility, no matter their source. Improvements in volatility treatment are therefore conflated with improvements in the mod …

If you have an American-exercise option and want to treat discrete dividends properly, you will have to apply some sort of technique for determining the exercise strategy. Mathematically this is phra …