Theory
The existence of a delta neutral portfolio was shown as part of the original proof of the Black–Scholes model, the first comprehensive model to produce correct prices for some classes of options. See Black-Scholes: Derivation.
From the Taylor expansion of the value of an option, we get the change in the value of an option, for a change in the value of the underlier :
-
- where (delta) and (gamma); see The Greeks.
For any small change in the underlier, we can ignore the second-order term and use the quantity to determine how much of the underlier to buy or sell to create a hedged portfolio. However, when the change in the value of the underlier is not small, the second-order term, cannot be ignored: see Convexity (finance).
In practice, maintaining a delta neutral portfolio requires continuous recalculation of the position's Greeks and rebalancing of the underlier's position. Typically, this rebalancing is performed daily or weekly.
Read more about this topic: Delta Neutral
Famous quotes containing the word theory:
“Osteopath—One who argues that all human ills are caused by the pressure of hard bone upon soft tissue. The proof of his theory is to be found in the heads of those who believe it.”
—H.L. (Henry Lewis)
“There is in him, hidden deep-down, a great instinctive artist, and hence the makings of an aristocrat. In his muddled way, held back by the manacles of his race and time, and his steps made uncertain by a guiding theory which too often eludes his own comprehension, he yet manages to produce works of unquestionable beauty and authority, and to interpret life in a manner that is poignant and illuminating.”
—H.L. (Henry Lewis)
“Hygiene is the corruption of medicine by morality. It is impossible to find a hygienest who does not debase his theory of the healthful with a theory of the virtuous.... The true aim of medicine is not to make men virtuous; it is to safeguard and rescue them from the consequences of their vices.”
—H.L. (Henry Lewis)