A call option on a stock has a delta of 0.7 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

To start, translate the positions into their delta effects. The trader is short 1000 calls with a delta of 0.7 each, so the total delta from the calls is -1000 × 0.7 = -700. The goal of delta-hedging is to bring the overall delta to zero by trading the put.

Option a: sell 400 puts. Each long put has a delta of -0.5, so selling puts (short puts) gives a positive delta contribution of +0.5 per put. For 400 puts, the delta added is +0.5 × 400 = +200. The combined delta would be -700 + (+200) = -500. This still leaves a net negative delta, so this choice does not hedge.

Option b: buy 400 puts. Buying puts adds a delta of -0.5 per put, so for 400 puts you add -0.5 × 400 = -200. The total delta becomes -700 + (-200) = -900. This over-weights the negative delta and moves further from hedging, so it is incorrect.

Option c: sell 1400 puts. Shorting puts yields a delta of +0.5 per put, so +0.5 × 1400 = +700. The total delta is -700 + (+700) = 0, achieving a delta-neutral hedge. This is the correct hedge amount.

Option d: buy 1400 puts. Buying puts adds -0.5 × 1400 = -700 delta, resulting in -700 + (-700) = -1400 total delta. This worsens hedging, as it doubles down on negative exposure.

In summary, only selling 1400 puts delivers a net zero delta when combined with the short calls, satisfying the delta-hedging objective while using the given put delta of -0.5.

FINS3635-Options, Futures & Risk Mgmt - T3 2025

A call option on a stock has a delta of 0.7 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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