Consider a two-period economy with annual risk-free interest rate of 3% in both periods. The current stock price is $100, and u=1.15 and d=0.75 for each period. (a) Find the current market value (at time 0) of an European call option on the stock with an exercise price of $90 that expires at the end of the second period. (b) Using the same method if valuation, find the current market value (time 0) of an European style put option on the stock price of $90 that expires at the end of the second period. (c) Use the put-call parity to derive the value of European style put option and compare it to the value you obtained in part (b).
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- Consider a European call option struck "at-the-money", meaning the strike price equals current stock price. There is one year until expiration and the risk-free annual interest rate is r = 0.06. We define the call option's "delta" as aCE(S,t) A as Is it possible to determine whether or not the call option's delta is greater than or less than 0.5?A European call that will expire in one year is currently trading for $3. Assume the risk-free rate (based on continuous compounding) is 5%, the underlying stock price is $60 and the strike price is $55. a. Is there an arbitrage opportunity? b. Describe exactly what a trader should do to take advantage of the arbitrage opportunity assuming it exists. c. Determine the present value of the profit that the trader can earn assuming you identify an arbitrage opportunity. Use at least four decimal places for those questions that require a numerical answer.Suppose the European call and put options with strike price $20 and maturity date in 1 month cost $2.0 and $1.0, respectively. The underlying stock price is $18 and the risk-free continuously compounded interest rate is 8%. (a) Is there an arbitrage opportunity? (b)If yes, how would you implement arbitrage opportunity?
- Calculate a one-year holding period return (HPR) for the following two investment alternatives: Which investment would you prefer, assuming they are of equal risk? Explain. The HPR for investment X is %. (Enter as a percentage and round to two decimal places.)Which of the following statements is (are) TRUE? Select one or more alternatives: If the AUD trades at a forward premium relative to the NZD, we would expect the NZD risk-free rate to be higher than the AUD risk-free rate. If the 1-year AUD risk-free rate is higher than the 1-year NZD risk-free rate then the value of the NZD will rise relative to the AUD over the next year. Assuming it doesn't hedge, a New Zealand based company importing Australian products will suffer if the value of the AUD rises relative to the NZD. □ If covered interest rate parity holds, then uncovered interest rate parity must also hold.Use Two-State Binomial Option (European) Pricing Model. Suppose you bought a stock today for $38.00. The stock price can either go up by a factor of 1.30 or down by a factor of 0.70 with equal probability in 0.50 years (or 180 days). Suppose the annual risk-free rate is 3.50% and the option exercise price is 35.00. How much should be the Call Option Value that expires in 0.50 years (or 180 days)?Enter your answer in the following format: 1.23Hint: The answer is between 6.74 and 9.38
- Find the current price of a one-year, R110-strike American put option on a non- dividend-paying stock whose current price is S(0) = 100. Assume that the continuously compounded interest rate equals r = 0.06. Use a two-period Binomial tree with u = 1.23, and d = 0.86 to calculate the price VP(0) of the put option.Suppose the following for European options: Stock price = $94 3-month call options with strike price $97 3-month put option with strike price $98 1-year risk-free rate is 3%. The put option is trading at $5 and there is a similar put option with an exercise price of $101 is trading at $8.5. The arbitrage gain that can be made is equal toYou are considering a European put option and a European call option on ABC Ltd and have available the following information. The put option with an exercise price of $15 and time to maturity of 60 days is priced at $2.00. The call option with the same exercise price and time to maturity is priced at $3.00. The underlying asset price is $15. The risk-free rate is 2% per 60 days. Could an arbitrage profit be earned? If so, how much the arbitrage profit is? Show your works (Hint: use discrete put-call parity equation and consider two scenarios for stock price at maturity of the options: $10 or $20).
- 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?Consider a European put and a European call option which are both written on a non-dividend paying stock, have the same strike price K = £80 and expire in T = 2 months. These options are trading for p = £21 and c = £30.80, respectively. The underlying stock price is S0 = £90. The continuously compounded risk-free rate of interest is r = 10% per annum. What is the present value of the arbitrage profit? Please explain your answer and show your workings. In your response, please show all cash flows (both today and at expiration) and explain why this is an arbitrage (i.e. risk-less) profit.Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option using the risk neutral approach. (d) Verify that the European call and European put prices found in (b) and (c) satisfy the put-call parity.