Question24 Holding all else constant, an increase in the volatility of the underlying asset will: Have no effect because market prices are already forward-looking Increase call option premiums but decrease put option premiums Increase both call and put option premiums Decrease both call and put option premiums ResetMaximum marks: 1 Flag question undefined

Question

BlackTom AI · Accepted Answer

Option premia depend positively on volatility; the sensitivity of an option’s price to volatility is called “vega,” and vega is positive for both calls and puts.

1. Relevant knowledge points and concepts
- Option value decomposes into intrinsic value + time value; volatility increases the time value because it raises the probability of extreme payoff outcomes.
- Black–Scholes partial derivatives show ∂C/∂σ = ∂P/∂σ = Vega > 0.
- Put–call parity (C - P = S - K e^{-rT}) ensures consistency between call and put prices but does not negate the volatility effect.

2. Complete reasoning process step by step
- Higher volatility increases the probability that the underlying’s terminal price will lie far above or far below the strike. For a call, that raises the chance of large positive payoff; for a put, it raises the chance of large payoff when the underlying falls.
- Therefore both option types gain value from increased uncertainty: calls benefit from upside scenarios, puts from downside scenarios.
- Mathematically under Black–Scholes: both call and put prices include σ in d1 and d2; differentiating with respect to σ yields the same positive vega.

3. Intermediate calculation steps (vega)
- Vega formula (Black–Scholes): Vega = S * sqrt(T) * φ(d1), where φ(d1) is the standard normal density at d1.
- Since S > 0, sqrt(T) > 0, and φ(d1) > 0, Vega > 0. This holds for both call and put, so ∂C/∂σ > 0 and ∂P/∂σ > 0.

4. Why the correct answer is correct
- The positive vega demonstrates both call and put premiums increase when volatility rises; increased volatility increases expected magnitude of payoffs on both sides, raising option prices.

5. Why other options are incorrect
- “Have no effect…” is wrong because volatility is a key input to option pricing and affects time value.
- “Increase call but decrease put…” is incorrect because both payoffs gain from greater dispersion; vega is positive for both.
- “Decrease both…” contradicts the positive vega result.

6. Conclusion
Therefore, an increase in the volatility of the underlying asset, holding all else constant, will increase both call and put option premiums, matching the provided answer.

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