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NISM Certifications · NISM-Series-VIII: Equity Derivatives · Basics of Derivatives

A stock is at Rs 800. The risk-free rate is 9% per annum with continuous compounding, and there are no dividends. Using the cost of carry model F = S x e^(rT), what is the approximate fair price of a 3-month futures contract? (Take e^0.0225 = 1.02275)

The fair futures price is about Rs 818.20. With a 9% rate and three months, rT is 0.0225, so the factor e^0.0225 is 1.02275. Multiplying Rs 800 by 1.02275 gives Rs 818.20. Using the full-year rate would overstate the price.

  1. ARs 800.00
  2. BRs 818.20Correct
  3. CRs 872.00
  4. DRs 836.00

Explanation

rT = 0.09 x 0.25 = 0.0225. F = 800 x 1.02275 = Rs 818.20. Rs 836 results from wrongly using a full year's rate of 9% on a quarter... actually 800 x 1.045 is wrong base for time; Rs 872 uses the full-year rate.

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