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CA Final · Advanced Financial Management · Derivatives Analysis and Valuation

A stock trades at ₹100. After one period it will be either ₹120 or ₹80. A European call with strike ₹100 expires at the end of the period. To replicate the call using the stock and borrowing, how many shares must be held (the hedge ratio or delta)?

The hedge ratio is 0.50 shares. Delta equals the spread in option payoffs (₹20 minus ₹0) divided by the spread in stock prices (₹120 minus ₹80), which gives 20/40 = 0.5. Holding half a share, financed partly by borrowing, replicates the call in both states.

  1. A0.25 shares
  2. B0.50 sharesCorrect
  3. C0.75 shares
  4. D1.00 share

Explanation

Call payoff is ₹20 in the up state and ₹0 in the down state. Delta = (20 − 0)/(120 − 80) = 0.5. Using 0.25 or 1.00 would not make the portfolio payoff match the call in both states.

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