In essence, delta is a measure of how long or short the holder of an option position is in terms of the underlying asset. A soft delta refers to a delta hedge which is implemented using options, and whereby delta vanishes asymptotically to the underlying asset price. Soft deltas are generally used to cover deltas caused by market moves (secondary deltas) that cannot be hedged with a hard delta without driving the risks up around the central delta value. Soft deltas always result from out-of-the-money (OTM) options, whose extrinsic value is zero, and has nothing but time premium.
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