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.

类似问题

Consider a put option and a call option written on the same stock and with the same strike price. Which of the following is true?

Call values increase as time until expiration increases.

If interest rates increase, put values also increase

An increase in the price of the underlying increases the value of both call and put options.

When determining their view on implied volatility in order to price an option, market-makers will consider:

Question at position 8 An excess of growth hormone (GH) before puberty can result in the development ofgigantism.Graves' disease.acromegaly.pituitary dwarfism.Clear my selection

Question at position 6 The most abundant supporting cells in the central nervous system are called Question Blank 1 of 1[input].

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单