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Dynamic hedging
By Martin | October 23, 2011
Replication of the payoff of a portfolio long the underlying and long a put by continuous delta hedging.
It started as a theory of Hayne Leland and Mark Rubenstein on the back of the Black-Scholes model.
It was used to provide put protection for equity portfolios at a time when portfolio puts were not available.
The theory assumed that an option position could be replicated by continuously adjusting the fraction of funds invested
in the underlying equities with the remainder invested in a risk-free asset.
An initial hedge of treasury bills was created, its size depending on the level of protection required.
If the portfolio value fell, stocks had to be sold and the hedge position increased; the opposite had to be done if its value rose.
The theory worked as long as volatility was predictable and low and while markets did not gap dramatically.
Since it relied on a large amount of trading in the underlying, it also required liquid markets and low bid/offer spreads.
The price discontinuity experienced in the 1987 crash caused such strategies to lose money and credibility.
Also known as portfolio insurance.
See delta hedging, static replication, replication.
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