Enter a T if the statement is true and F if it is false. 1. The payoff of a European put option with strike $50 is $50 if the stock price at maturity is $100. 2. The payoff of a European call option with strike $50 is $50 if the stock price at maturity is $100.
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- In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49Assume that the current price of a stock is S0 = 100. An investor holds long one European put option with a strike price of K = 100 and short one European call option with strike K = 105. Both options mature at the same time T. Assume that the stock price at maturity is ST = 102. What is the payoff to the investor? Select one: a. 2 b. 1 c. 0 d. -1 e. -2 f. None of the abovePreviously, you purchased a European put option on Parlicoot Inc shares. The option has just matured. The strike price on the option is 98.17, while the current stock price is 89.19. What is your payoff?
- An investor buys a European call option at a price of 7.6 yuan. The stock price is 52 yuan and the strike price is 55 yuan. Under what circumstances will the investor make a profit ? Under what circumstances will the option be executed ? Draw a diagram of the relationship between investor profitability and stock price at maturity.Let C be the price of a call option that enables its holder to buy one share of a stock at an exercise price K at time t; also, let P be the price of a European put option that enables its holder to sale one share or the stock for the amount K at time t. Let S be the price of the stock at time 0. Then, assuming that interest is continuously discounted at a nominal rate r, either S+P-C=Ke-rt or there is an arbitrage opportunity. Question: How do I verify that the strategy of selling one share of stock, selling one put option, and buying one call option always results in a positive win if S+P-C>Ke-rt ?Consider a European call on Procter and Gamble stock (PG) that expires in one period. The current stock price is $120, the strike price is $130, and the risk-free rate is 5%. Assume that PG stock will either go up to $150 (probability = .4), or go down to $90 (probability = .6). Construct a replicating portfolio based on shares of PG stock and a position in a risk-free asset, and compute the price of the call option.
- Consider a portfolio that consists of the following four derivatives: 1) a put option written(sold) with strike price K − 5, 2) a call option purchased with strike price K − 5, 3) a call option written(sold) with strike price K + 5, and 4) a put option purchased at strike price K + 5. All options are European.The risk-free rate is rf , the time to expiration is T, the initial stock price is S0, and the stock price atmaturity is ST . What are the payoffs at expiration of this portfolio? What must the price of this portfoliobe?Using put-call parity formula, derive expressions for the lower bounds for European call and put options. What is a lower bound for the price of (i) a three-month call option on a non-dividend-paying stock when the stock price is R860, the strike price is R760, and the risk-free interest rate is 10% per annum? (ii) a three-month European put option on a non-dividend-paying stock when the stock price is R500, the strike price is R610, and the discrete risk-free interest rate is 9% per annum?Suppose a one-year European put option on a stock has an exercise price of $30 and oneyear European call option on the same stock has the same exercise price of $30. The call is worth 3$ and the put is worth 2$. If the one-year interest rate is 1.5%, what is the price of the underlying stock, assuming no arbitrage opportunity?
- You observe the price of a European put option that expires in nine months and has a strike price of$45 is $3. The underlying stock price is $49.50. The term structure is flat, with all risk-free interestrates being 8%.a. What is the price of a European call option that expires in nine months and has a strike priceof $45? b. You observe next that the price of the call option (in part (a)) in the market is $9.59. Statewhy an arbitrage opportunity exists and explain how you would take advantage of thisopportunity. (Hint: answer should include an outline general strategy, net cost ofstrategy at initiation and net profit at expiration using the numbers in the question)Assume a stock is selling for GH¢48.50 with options available at 40, 50, and 60 strike prices.The 50 call option price is at 2.75.a. What is the intrinsic value of the 50 call?b. Is the 50 call in the money?c. Are the 40 and 60 call options in the money?A trader buys a European put on a share for K3. The stock price is K42 and the strike price is K40. State the circumstances under which the trader will make a profit. State the circumstances under which the option will be exercised. Draw a diagram in support of your answers above, showing the variation of the trader’s profit with the stock price at the maturity of the option