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CA Final · Advanced Financial Management · Derivatives Analysis and Valuation

A broker writes 5,000 European call options on Meridian Ltd, each on one share, and wants to be delta-neutral. The share price is Rs 500, each call is valued at Rs 62 by Black-Scholes, and N(d1) = 0.60. The hedge is formed by buying shares and financing any shortfall after using the premium received by borrowing. How much must be borrowed?

The broker must borrow Rs 11,90,000. The delta hedge needs 5,000 × 0.60 = 3,000 shares costing Rs 15,00,000. The premium of Rs 3,10,000 received on the 5,000 written calls reduces the financing, leaving Rs 11,90,000 to be borrowed.

  1. ARs 11,90,000Correct
  2. BRs 15,00,000
  3. CRs 21,90,000
  4. DRs 18,10,000

Explanation

Delta of written calls = 5,000 × 0.60 = 3,000 shares to buy, costing 3,000 × 500 = Rs 15,00,000. Premium received = 5,000 × 62 = Rs 3,10,000. Borrowing = 15,00,000 − 3,10,000 = Rs 11,90,000. Rs 21,90,000 arises from buying 5,000 shares (full number of options) instead of delta-adjusted shares.

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