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CA Final · Advanced Financial Management · Derivatives Analysis and Valuation

Arjun Securities values a 1-year European call on a non-dividend share with S = Rs 800, X = Rs 800, continuously compounded risk-free rate 5% and volatility 25%. It has computed d1 = 0.325 and d2 = 0.075, with N(d1) = 0.6274 and N(d2) = 0.5299. Given e^-0.05 = 0.951229, what is the Black-Scholes call value?

The call is worth about Rs 98.67. Black-Scholes gives S x N(d1) minus the discounted strike times N(d2): 501.92 less 760.98 x 0.5299, which is 403.25. Omitting the discount factor or using N(d1) in both terms gives wrong values.

  1. ARs 98.67Correct
  2. BRs 78.00
  3. CRs 24.48
  4. DRs 39.02

Explanation

C = S N(d1) - X e^-rt N(d2) = 800 x 0.6274 - 800 x 0.951229 x 0.5299 = 501.92 - 403.25 = Rs 98.67. Rs 78.00 results from not discounting the strike; Rs 24.48 results from using N(d1) for both terms.

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