CA Final · Advanced Financial Management · Risk Management

An Indian bank has written 2,000 call options (each on 1 share) with delta 0.50 and gamma 0.04. It is delta-hedged using shares. It wants to also be gamma-neutral using a traded option with delta 0.40 and gamma 0.05 per option. Which action achieves gamma neutrality, and what is the number of traded options involved?

The bank should buy 1,600 traded options. Its short calls carry gamma of -80 (2,000 x 0.04), and each traded option adds 0.05, so 80 divided by 0.05 gives 1,600 long options to bring the portfolio gamma to zero.

ABuy 1,600 traded optionsCorrect
BSell 1,600 traded options
CBuy 2,500 traded options
DBuy 1,000 traded options

Explanation

The short calls give gamma = -2,000 x 0.04 = -80. To offset, need +80 gamma from traded options: 80 / 0.05 = 1,600 bought. Selling would worsen the negative gamma. 2,500 wrongly divides 100 or uses 0.04 reversed ratios; 1,000 uses delta values incorrectly. After this, shares must be readjusted for delta.

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