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Delta Hedging : A first Attempt
Issued on April 10 2010 par Strategies-options.com

Option Price moves with the underlying. To hedge this risk, it's necessary to find a way in order to erase its correlation with that one.
Hedging, unless stop trading, means to find a correlation relationship between what we have in our portfolio and other securities or financial products in order to build a global portfolio with a much less volatil P&L if things have to go on the bad side.



I - Option Delta : As a Correlation between Underlying and Option

We have seen that it's possible to approximate option variations using a first order Taylor expansion.

For a small period, it leads to :

dV ≈ Δ . dS

dV is the option variation
Δ is the correlation coefficient between option and underlying, option delta.
dS a small spot variation.

What we need is a global variation almost nil, a global delta that is worth 0.

Hence, hedging a portfolio made of one long option with a delta Δ is using a portfolio with a delta Δ' = - Δ .



II - Different Ways in order to Delta Hedge

Several instruments exhibit a delta.

a - Hard Delta Instrument
Hard Delta is a delta that correspond to a ( almost ) linear exposition. This is the case with futures, formard, spot...This delta remains steady.

b - Soft Delta Instrument
It's broadly the case with options which have a non linear exposition to the underlying. Soft Delta is a 'moving delta'.



Next : Delta Hedging
Previous :Delta Hedging Principles



Hedging : Principles
Delta Hedging Principles
Gamma Hedging Principles
Vega Hedging Principles

Hedging : A First Attempt
Delta Hedging : A First Attempt
Gamma Hedging : A First Attempt

Hedging
Delta Hedging


Related Pdf :

- Delta hedging - Theory and Application
- Optimal Process Approximation: Application to Delta Hedging and Technical Analysis
- Delta Hedging with Black-Scholes Model


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