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The condition $$ud=1\text{, or equivalently }u=1/d$$ is necessary to ensure convergence of the Binomial tree's mean $\mu$ and standard deviation $\sigma$ to nonfinite values when $n$ (number of steps) goes to infinity. Cox-Rubinstein-Ross showed in their famous paper, that to achieve this, we must have: u=e^{\sigma\sqrt{t/n}}\text{, ...

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The issue is what exchanges recognize as acceptable complex option orders. This is governed by FINRA margin rules like rule 4210 Brokers can only execute orders that are recognized by options exchanges. So what brokers can put on a single order ticket is limited. The most complex spreads defined by FINRA rules would be butterfly spreads, box spreads and ...

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Under the Black-Scholes framework, you can calculate the implied volatility, given the option's price, underlying's price, time to maturity and the risk free rate. To calculate the implied volatility you have to use a root finding method, since there is not a closed form of the inverse of the B-S option pricing equation for volatility. In the real world ...

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There is no such thing as "free" option data. This is free -->http://www.nasdaq.com/symbol/aapl/option-chain You could crawl that. But to get the actual ticks or intraday data, you will unfortunately have to pay. I strongly suggest you find a college business program that has option data ticks and reach out to them. Best of luck, JL

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All complex multi leg options strategies involve being both long and short options. In other words to enter into a multileg position one is both buys options and sells other options. Therefore it is confusing to think of spreads (2 legs), butterflies (3 legs) and condors(4 legs) as buying them or selling them. Step back and reason what you want to ...

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