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Dividend estimation and forecast is not an easy problem. This paper describes and compares few approaches. If the company pays dividend according to a certain scheme (quarterly, annually, etc.), it's easy to forecast a future dividend yield, using last known paid amount and the underlying price. In some cases (like European and Asian companies), the ...


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In real life, you imply the unknown dividend yields from the forwards and the discount curve.


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If it is a real example, then it may be unnecessary to consider the dividend explicitly. After all, the Gordon formula states that the stock price is equal to the discounted future cash flow of dividends. For instance, if I have a call at strike K and the future dividend is announced when the market didn't expect it, then most likely the spot price will go ...


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To provide a straight forward answer: It is not a good model. It never was, it never will be. Until we all do not come up with a better model that provides better modeling accuracy while it is equally intuitive and makes similarly simplifying assumptions the BS model with its geometric brownian motion component is here to stay. It actually does not matter ...


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The following paper gives you really all of the missing steps in a very detailed form: Black-Scholes Option Pricing Formula by Michael Tomas and Ravi Shukla From the paper: "This presentation is purely for pedagogical purposes. In the course of doing work on option pricing, we found no complete solution for the Black-Scholes model. By complete, we mean ...


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Basically, Black-Scholes is an "industry standard" formula. It is widely used by practitioners and usually augmented with extra specifications or intuition. It has a closed form solution, which is rare in option pricing models. It is also relative to simple to understand. Otherwise, you usually need to rely on Monte Carlo simulation or some other way. And ...


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Brownian motion - because it is simple, and results in intuitive closed form solutions, and it's not a terrible description of asset prices, especially when employed in high-frequency event time. Geometric - because the returns compound, and equities cannot go below zero due to the fact that they are limited liability corporations There are many, many ...


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If at first you don't have a model at all, then geometric Brownian motion is not bad. As others before me said: log-returns are normally distributed in this model. This is debatable and there are times and markets where this is not true. There is more than enough research about this. But why is a model based on Brownian motion not that bad? The reason is ...


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The normal distribution is very powerful distribution: By the central limit theorem, the mean of any large sample always converges to the normal distribution Considering the most simplistic Binomial Tree model, where price goes only up or down each period, it can be shown that the distribution of returns of this tree converges to Normal for infinetesimal ...


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So Black-Scholes came around and it made pricing options mathematically viable in a (seemingly) objective sense. The assumptions underlying the model are flawed, but they work reasonably well in a lot of market environments. The problem lies in when normal market conditions start to change character. When things start to get wacky, like when a giant selloff ...


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Jaeckel has a paper "Let's be rational" in which he "show how Black’s volatility can be implied from option prices with as little as two iterations to maximum attainable precision on standard (64 bit floating point) hardware for all possible inputs.". I guess it doesn't qualify as closed-form for you, though one might argue that having to apply a ...


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The method described in Hallerbach (2004) always worked well for me. We derive an estimator for Black-Scholes-Merton implied volatility that, when compared to the familiar Corrado & Miller [JBaF, 1996] estimator, has substantially higher approximation accuracy and extends over a wider region of moneyness.



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