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There is a little known Greek called "lambda" or leverage which equals Delta times Stock price divided by option price $\lambda=\frac{\Delta . S}{c}$. So if $\lambda>1$ the option could be said to be leveraged, meaning the dollar value of a delta equivalent amount of stock is greater than the market value of the option.


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Let's say you have 100k USD account and trade some futures, which monetary volume is about 100+/-10k. To trade it you actually need only a ~10 000 for maintenance margin. So on your 100k you can open 10 contracts, it means the leverage will be 10. The same is for options. Options on futures require maintenance margin and it maight be compared to the ...


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In general any investment position is said to be leveraged, if it is financed by a debt position. This is with regards to options, stocks or any other security. Say you buy an option with maturity in one year at a premium of 100 USD, hold it to maturity and get a payoff of 120. You will have a profit of 20 USD, or 20% of your invested capital. Instead you ...


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For a mathematical model you can have a look at this paper: The Valuation of Compound Options by Robert Geske where after equation (17) it is shown that $\partial \sigma_s/\partial S<0$.



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