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CA Final · Advanced Financial Management · Derivatives Analysis and Valuation

A dealer writes 2,000 one-period European call options on Meghdoot Ltd. The spot price is ₹1,000, and next period it will be either ₹1,300 or ₹900. The strike is ₹1,000. To remain delta-neutral at inception, how many shares should the dealer buy?

The dealer should buy 1,500 shares. The hedge ratio is the payoff spread divided by the price spread, 300/400 = 0.75 share per call. Multiplied by 2,000 written calls, this gives 1,500 shares, which makes the position riskless across both outcomes.

  1. A1,500 sharesCorrect
  2. B600 shares
  3. C2,000 shares
  4. D1,000 shares

Explanation

Call payoffs are 300 and 0. Delta = (300−0)/(1,300−900) = 0.75 share per call. For 2,000 calls the hedge is 2,000×0.75 = 1,500 shares. Buying 600 would result from using a wrong delta of 0.3, and 2,000 would assume a delta of 1.

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