Question15 Other things equal, the price of a stock call option is positively correlated with the following factors except: Select one alternative: A. the exercise price. B. the stock volatility. C. the time to expiration. D. the stock price. E. None of the above is correct. ResetMaximum marks: 2 Flag question undefined单项选择题
A
A. the exercise price.
B
B. the stock volatility.
C
C. the time to expiration.
D
D. the stock price.
E
E. None of the above is correct.

Question

Question15 Other things equal, the price of a stock call option is positively correlated with the following factors except: Select one alternative: A. the exercise price. B. the stock volatility. C. the time to expiration. D. the stock price. E. None of the above is correct. ResetMaximum marks: 2 Flag question undefined单项选择题

A

A. the exercise price.

B

B. the stock volatility.

C

C. the time to expiration.

D

D. the stock price.

E

E. None of the above is correct.

BlackTom AI · Accepted Answer

For a European call option, the option price increases with the underlying stock price, volatility, and time to expiration, but decreases with the strike (exercise) price. 1. Relevant knowledge points and concepts - Black–Scholes formula (for a European call): C = S·N(d1) − K·e^(−rT)·N(d2). N(·) is the standard normal CDF. - Sensitivities (Greeks): Delta ∂C/∂S = N(d1) > 0 (call price rises with S). Vega ∂C/∂σ > 0 (call price rises with volatility). Partial derivative wrt K: ∂C/∂K = −e^(−rT)·N(d2) < 0 (call price falls as K increases). Time to expiration generally increases optionality (longer T gives greater value). 2. Step-by-step reasoning - Option D (stock price): ∂C/∂S = N(d1), which is strictly positive between 0 and 1. So call price is positively correlated with S. - Option B (volatility): Vega > 0 because greater volatility increases the probability of finishing in-the-money; therefore call value rises with σ. - Option C (time to expiration): More time increases the chance of favorable movements and increases Vega (Vega ∝ S·√T·n(d1)), so all else equal longer T increases call value. - Option A (exercise price): From ∂C/∂K = −e^(−rT)·N(d2) the derivative is negative, so an increase in K reduces the call price. 3. Intermediate relationships shown - C = S·N(d1) − K·e^(−rT)·N(d2) - ∂C/∂S = N(d1) > 0 - ∂C/∂σ = Vega > 0 (proportional to S·√T·n(d1)) - ∂C/∂K = −e^(−rT)·N(d2) < 0 4. Why the correct answer is correct Because all listed factors except the exercise price increase the call’s value when they increase. The exercise (strike) price works in the opposite direction: a higher strike makes it harder for the option to finish in-the-money, so the call’s price falls. 5. Why other options are incorrect - B, C, D each describe variables that increase call value (positive correlation), so they are not exceptions. - E is incorrect because there is indeed one correct exception (A). 6. Conclusion The correct answer is A. the exercise price. This matches the provided answer.