Abstract
The price of options changes when certain influencing factors change. So-called risk indicators are used to describe these price changes.
The ability, to which people attach mostimportance, is the ability to pay.
Oscar Blumenthal (1852–1917), German writer
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Notes
- 1.
There are, however, also risk indicators that have names such as vega, vomma, zomma, or vanna. These are not Greek letters, of course.
- 2.
“Approximately” since (partial) derivatives of functions are always linearizations (i. e. linear approximations of the function) or—geometrically speaking—because the graph of the function is replaced by the tangent line to it.
- 3.
This is due to the simplifying assumptions; in many other situations, a calculation can only be made using numerical solution methods.
- 4.
Of course, the chance that the option price decreases gets also higher; however, the payout is bounded below by zero, but unbounded above.
- 5.
Negative numbers mean sale, so that \(\frac {\Gamma _1}{\Gamma _*}\) calls and Δ0 shares are sold and \(\frac {\Gamma _1}{\Gamma _*}\Delta _*\) shares are bought.
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Korn, R., Luderer, B. (2021). The Greeks and the Risk: About Risk Indicators for Stock Options. In: Money and Mathematics. Springer Texts in Business and Economics. Springer, Wiesbaden. https://doi.org/10.1007/978-3-658-34677-5_47
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DOI: https://doi.org/10.1007/978-3-658-34677-5_47
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