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ACCA Strategic Professional · Advanced Financial Management · Application of option pricing theory in investment decisions

Using the Black-Scholes model, the volatility of the underlying share rises while all other inputs stay unchanged. What happens to the values of a European call and a European put on that share?

Both the call and the put rise in value. Higher volatility widens the range of possible share prices at expiry, while the holder's loss is capped at the premium paid, so the chance of a large payoff increases for both kinds of option.

  1. ABoth the call and the put increase in valueCorrect
  2. BThe call increases and the put decreases in value
  3. CThe call decreases and the put increases in value
  4. DNeither changes, because volatility affects only the time value of American options

Explanation

Option holders gain from favourable price movements but their loss is limited to the premium. Higher volatility therefore raises the chance of a large payoff for both calls and puts. This is why vega is positive for both. The idea that only American options are affected is wrong, because European options also gain time value from volatility.

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