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Which of the following statements is correct?
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A) The gamma of a long position in a European option takes the highest value for deep in-the-money options. |
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B) The delta of a short position in a European put is between -1 and 0. |
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C) The delta of a long position in a deep in-the-money European put is close to zero. |
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D) The gamma and the vega of a long position in a European put are positive. |
Please explain and justify your choice.
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- 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 putState 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…A European call option has a strike price of K and maturity of T. If the stock price at the maturity is ST, what is the payoff from a short position in this call option (without considering the option price)? Group of answer choices: Max(K - ST, 0) -Max(ST - K, 0) -Max(K - ST, 0) Max(ST - K, 0)
- 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.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.In this problem, we derive the put-call parity relationship for European options on stocks that pay dividends before option expiration. For simplicity, assume that the stock makes one dividend payment of $D per share at the expiration date of the option.a. What is the value of a stock-plus-put position on the expiration date of the option?b. Now consider a portfolio comprising a call option and a zero-coupon bond with the same maturity date as the option and with face value (X + D). What is the value of this portfolio on the option expiration date? You should find that its value equals that of the stock-plus-put portfolio regardless of the stock price.c. What is the cost of establishing the two portfolios in parts (a) and (b)? Equate the costs of these portfolios, and you will derive the put-call parity relationship.
- Consider the Black-Scholes model. In class, we derived the formula for the price of the European Call option. (a) Using the formula for the European Call option, calculate the Greek Delta. (b) Using the formula for the European Put option, calculate the Greek Delta.1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.Imagine a situation where European options on some underlying stock have the following relationship. p+S > c+ K*exp(-rT). (a) Describe the arbitrage opportunities that are available with an example. (b) Now change those options to American-style options. Does the arbitrage strategy still work? Explain your answer.
- i)identify, analyze and discuss the following characteristics of an American put option: maximum value, intrinsic value, time value, lower bound, and payoff at expiration. ii) analyze and discuss the following factors on an American put option: time to expiration, exercise price, interest rate, volatility, and dividends. iii) identify, analyze, and discuss the following characteristics of a European call option: maximum value, intrinsic value, time value, lower bound, and payoff at expiration. iv) analyze and discuss the following factors on a European call option: time to expiration, exercise price, interest rate,The binomial and Black-Scholes pricing models are the "guide posts" for pricing American and European options. Investors often consider employing stock options in their portfolios to minimize risk. They are viewed as "insurance" against losses in the portfolio. What are the pros and cons of the two models when pricing options? How would you incorporate the two models in your investment strategies/plans?Michael Weber, CFA, is analyzing several aspects of option valuation, including the determinants of the value of an option, the characteristics of various models used to value options, and the potential for divergence of calculated option values from observed market prices.a. What is the expected effect on the value of a call option on common stock if the volatility of the underlying stock price decreases? If the time to expiration of the option increases?b. Using the Black-Scholes option-pricing model and an estimate of stock return volatility, Weber calculates the price of a 3-month call option and notices the option’s calculated value is different from its market price. With respect to Weber’s use of the Black-Scholes option-pricing model,i. Discuss why the calculated value of an out-of-the-money European option may differ from its market price.ii. Discuss why the calculated value of an American option may differ from its market price.