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.
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- 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?Under the assumptions of the Black-Scholes model, which value does not affect the price of a European call option: Select one: a. the interest rate r b. the spot price S c. the strike price K d. the return of the stock µ e. the volatility of the stock σThis is an open ended question and you need to do some research to get the answers: Is arbitrage good or bad? Justify. What are some problems with the Black-Scholes-Merton model? Suggest some improvements of the Black-Scholes-Merton model. In the class, we have derived the Black-Scholes-Merton formula for European options. Is is possible to derive something similar for American options?
- 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.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.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 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.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 putFinance Use the put-call parity to derive the relationship between the theta of a European call option and the theta of a European put option. Show that the relationship holds if you substitute the formulas for theta of call and theta of put in the Black-Scholes model.
- Which of the following is true: The BSM model combined with the put call parity can be used to give the theoretical price of an American put option. One of the variables that influences the price of the option is the expected return on the stock. Since dividends could trigger an early exercise of an American call, the BSM formula dividend adjustment will provide the correct price of an American call. The BSM formula requires cumulative probabilities from the lognormal distribution. The BSM model may be used with currency options by replacing the dividend yield with the foreign interest rate.a. Explain the covered call options strategy b. Graphically show a covered call options strategy, including payoff. Explain why an investor mayuse this option strategy.c. Using put-call parity, explain the shape of the payoff line (in part (a) of this question). Whatoption position does it look like and why?Derive the Crank-Nicolson's finite difference method to solve the Black-Scholes-Merton partial differential equation for pricing an American put option. Note: Make sure you have described the grid, discretization of various derivatives and then combined them suitably to get a scheme.]