A call option on a stock has a delta of 0.4 and a trader has just sold 1000 calls. The trader decides to delta-hedge his call position by trading a put on the same underlying. What position should the trader take in the put to delta-hedge her call position if the put delta is -0.5?

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BlackTom AI · Accepted Answer

First, translate the given deltas into a hedge target. The trader has sold 1000 calls with a delta of 0.4 each, so the total call delta position is +400 (since selling calls yields a negative exposure, but delta effectively offsets the stock movement; in hedging terms we consider the absolute delta to neutralize). To delta-hedge, we need to offset this +400 with an opposite delta.
Option A: sell 400 puts. Each put has delta -0.5, so selling puts would add +0.5 per put to the position. 400 puts would add +0.5 × 400 = +200 delta. Net delta would be 400 + 200 = +600. This worsens hedging, not neutralizes it.
Option B: buy 400 puts. Buying puts adds negative delta: -0.5 × 400 = -200. Net delta would be 400 - 200 = +200. Still not hedged to zero.
Option C: sell 800 puts. Selling puts adds +0.5 × 800 = +400 delta. Net delta would be 400 + 400 = +800. Far from neutral.
Option D: buy 800 puts. Buying 800 puts adds -0.5 × 800 = -400 delta. Net delta would be 400 - 400 = 0, achieving a delta-neutral position.
Thus, the hedge requires purchasing 800 puts to offset the 400-delta exposure from the sold calls.

FINS3635-Options, Futures & Risk Mgmt - T3 2025

A call option on a stock has a delta of 0.4 and a trader has just sold 1000 calls. The trader decides to delta-hedge his call position by trading a put on the same underlying. What position should the trader take in the put to delta-hedge her call position if the put delta is -0.5?

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