IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model
A bank has sold 1,000 European call options on a non-dividend-paying share, each on one share. The call delta is 0.60. To be delta-neutral, which position in the share should the bank hold?
The bank should be long 600 shares. The 1,000 written calls have a combined delta of -600, so buying 600 shares offsets it and makes the portfolio delta-neutral. Using 1 minus delta, giving 400, is a mistake.
- AShort 600 shares
- BLong 400 shares
- CLong 1,000 shares
- DLong 600 sharesCorrect
- Short 400 shares
Explanation
The short calls have a portfolio delta of -1,000 x 0.60 = -600. Holding +600 shares gives total delta zero. Long 400 shares would result from wrongly using 1 - delta.
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