Which of the following is NOT true? A) Implied volatility calculated from a European call option should be the same as that calculated from a European put option when both have the same strike price and maturity B) Implied volatility for out of the money put options on equity is usually higher than implied volatility for out of the money call options on equity with the same maturity C) A volatility smile implies that both tails of the implied risk neutral distribution are fatter than the lognormal distribution D) A volatility skew implies that implied volatility for out of the money call options is higher than that for at the money call options

Which of the following is NOT true? A) Implied volatility calculated from a European call option should be the same as that calculated from a European put option when both have the same strike price and maturity B) Implied volatility for out of the money put options on equity is usually higher than implied volatility for out of the money call options on equity with the same maturity C) A volatility smile implies that both tails of the implied risk neutral distribution are fatter than the lognormal distribution D) A volatility skew implies that implied volatility for out of the money call options is higher than that for at the money call options

International Financial Management

14th Edition

ISBN:9780357130698

Author:Madura

Publisher:Madura

Chapter7: International Arbitrage And Interest Rate Parity

Section: Chapter Questions

Problem 4BIC

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State whether the following statements are true or false. In each case, provide a brief explanation. a. In a risk averse world, the binomial model states that, other things being equal, the greater the probability of an up movement in the stock price, the lower the value of a European put option. b. By observing the prices of call and put options on a stock, one can recover an estimate of the expected stock return. c. An investor would like to purchase a European call option on an underlying stock index with a strike price of 210 and a time to maturity of 3 months, but this option is not actively traded. However, two otherwise identical call options are traded with strike prices of 200 and 220 respectively, hence the investor can replicate a call with a strike price of 210 by holding a static position in the two traded calls. d. In a binomial world,if a stock is more likely to go up in price than to go down, an increase in volatility would increase the price of a call option and reduce…
Which of the following statements is correct? As the volatility of the stock price increases (all else remaining unchanged), both European calls and puts become less valuable. The seller of an option can choose whether to post a margin or not. Consider a call and a put which are both written on the same asset, and have the same strike price and the same time-to-maturity. It is possible for the call and the put to be out-of-the-money at the same time. The intrinsic value of a European option is the value it would have if the time-to-maturity was zero. Please explain and justify your choice using your own words.
Could you help giving me explanations on this quant finance problem? Which of the following statement about the one-step binomial tree-model are correct ? Select all correct options. A. The stock's expected return does not play any role for the arbitrage-free pricing of an option written on the stock. B. Arbitrage-free prices of European stock options can be computed as expected values of the discounted payoff of the option of maturity by using the risk-neutral probability. C. The seller of a European stock option can perfectly hedge herself against the risk of paying the payoff to the holder of the option at maturity by implementing a hedging strategy which perfectly replicates the payoff at maturity by trading the underlying stock.
Which of the following statements about European option contracts is TRUE? a. Typically American options are cheaper than otherwise similar European options due to the uncertainty regarding the date of exercise. b. One can synthesise a long forward position in the underlying by being long a call and short a put c. A long call position and a short put position both involve buying the underlying and so are equivalent d. The price of an option can be obtained by computing the true probabilities of each state of nature, working out the expected option payoff across those states and then discounting back to the present.
My question is for a synthetic call option why do we need to borrow the present value of the strike price and what does it mean in a simple language explanation. Similarly why do we need to lend the present value of the stock at risk-free rate and what does it mean in simple language explanation? Please also clarify the significance of risk free rate? Why is it used in put call parity. Synthetic Call Option: If an investor believes that a call option is over-priced, then he/she can sell the call on the market and replicate a synthetic call. Borrow the present value of the strike price at the risk free rate and purchase the underlying stock and a put. Synthetic Put Option: Similar to the synthetic call option. A synthetic put can be created by re-arranging the put-call parity relationship, if the trader believes the put is overvalued. Synthetic Stock: A synthetic stock can also be created by rearranging the put-call parity identity. In this case, the investor will buy the…
Problem 4a: State whether the following statements are true or false. In each case, provide a brief explanation. a. In a risk averse world, the binomial model states that, other things being equal, the greater the probability of an up movement in the stock price, the lower the value of a European put option.
Part I. Explain why an American call options on futures could be optimally exercised early while call options on the spot can not be optimally exercised. Assume that there is no dividend. Explain how to use call options and put options to create a synthetic short position in stock. Part II. Indicate whether each of the following two statements below is true, false or uncertain and justify your response. It is theoretically impossible for an out-of-money European call and an in-the-money European put to be trading at the same price. Both options are written on the same non-dividend paying stock. A 3-month European put option on a non-dividend-paying stock is currently selling for $3.80. The stock price is $48.0, the strike price is $51, and the risk-free interest rate is 6% per annum (continuous compounding). There is no arbitrage opportunity in this scenario.
Referring to put-call parity, which one of the following alternatives would allow you to create (own) a syntheticEuropean call option? Sell the stock, buy a European put option on the same stock with the same exercise price and the same maturity, invest an amount equal to thepresent value of the exercise price in a pure-discount riskless bond Buy the stock, sell a European put option on the same stock with the same exercise price and the same matunty: short an amount equal to the presentvalue of the exercise price worth of a pure-discount riskless bond Buy the stock, buy a European put option on the same stock with the same exercise price and the same maturity; short an amount equal to the presentvalue of the exercise price worth of a pure-discount riskless bond
Suppose that C is the price of a European call option to purchase a security whose present price is S.Show that if C > S then there is an opportunity for arbitrage (i.e. riskless profit). You may assume theinterest rate is r = 0 so that present value calculations are unnecessary.
Select all of the following statements that accurately compare or contrast forwards and options: Group of answer choices Taking naked long positions in either a call or forward will lead to an overall long position in the underlying security. Options and forwards always have identical payoffs if the spot price remains the same. Both options and forwards can be used to reduce exposure to foreign exchange risk. Going long a naked put option and going short a naked forward both cause unlimited liability. Both options and forwards require the payment of a premium at the initiation of the contract. Forward contracts impose obligations on both parties in the transaction. Options contracts only impose an obligation on one party.
Which of the following statements about European option contracts is true? Question 2Answer a. Typically American options are cheaper than otherwise similar European options due to the uncertainty regarding the date of exercise. b. The price of an option can be obtained by computing the true probabilities of each state of nature, working out the expected option payoff across those states and then discounting back to the present. c. A long call position and a short put position both involve buying the underlying and so are equivalent d. One can synthesise a long forward position in the underlying by being long a call and short a put
Which of the following statements is correct? A) The gamma of a long position in a European option takes the highest value for deep in-the-money options. B) The delta of a short position in a European put is between -1 and 0. C) The delta of a long position in a deep in-the-money European put is close to zero. D) The gamma and the vega of a long position in a European put are positive. Please explain and justify your choice.