Question text 2Marks Call options and put options are written on Qantas.If the interest rate increases, how are the prices of Qantas options affected?Qantas call options will Answer 4[select: , increase, decrease] while Qantas put options will Answer 5[select: , decrease, increase]. Notes Report question issue Question 10 Notes多项填空题
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Question

Question text 2Marks Call options and put options are written on Qantas.If the interest rate increases, how are the prices of Qantas options affected?Qantas call options will Answer 4[select: , increase, decrease] while Qantas put options will Answer 5[select: , decrease, increase]. Notes Report question issue Question 10 Notes多项填空题

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我们收录了全球超50000道真实原题与详细解析,现在登录,立即获得答案。

BlackTom AI · Accepted Answer

Put–call parity is the key relation: C − P = S − K e^(−rT), where C and P are European call and put prices, S is the spot price, K the strike, r the continuously compounded risk‑free rate, and T time to maturity.

Differentiate both sides with respect to r:
d/d r (C − P) = d/d r (−K e^(−rT)) = K T e^(−rT) > 0.
Thus an increase in r raises (C − P). From Black–Scholes option Greeks the individual sensitivities are
∂C/∂r = T K e^(−rT) N(d2) > 0
and
∂P/∂r = −T K e^(−rT) N(−d2) < 0,
so calls have positive sensitivity to r while puts have negative sensitivity.

Intuition: higher interest rates reduce the present value of the strike payment K (K e^(−rT) falls), so it becomes cheaper in present‑value terms to exercise a call in the future — increasing call value. Conversely, a put (the right to sell at K) becomes less valuable when the discounted strike is lower, so put value falls. Another way to see it: higher r increases forward expected asset price (F = S e^{rT}), making upside (calls) more attractive and downside (puts) less attractive.

Caveat: this standard result applies to European options (and typically to non‑dividend or modestly dividend‑paying stocks under standard option pricing). Exceptional contract features or early exercise considerations on dividend‑paying stocks can modify magnitudes but not the basic sign relationship.

Why the other ordering is wrong: reversing the signs (calls decrease and puts increase) contradicts put–call parity, Black–Scholes Greeks, and the present‑value intuition above.

Conclusion: Qantas call option prices will increase while Qantas put option prices will decrease, matching the provided answer.

类似问题

When the non-dividend paying stock price is $40, the strike price is $42, the risk-free rate is 3% p.a. (continuously compounded), the volatility is 25% and the time to maturity is 6 months, which of the following is the price of a European call option on the stock?[Fill in the blank]

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