We observe the prices (at time t = 0) of the following European call/put options on the market. Suppose that the interest rate r = 0, and the initial price of the underlying stock is So= 100. Please construct a portfolio, using these options together with the cash (bank account), to find an arbitrage opportunity. Option Type Strike Put 90 Call 100 Put 110 Maturity Option Price at time t=0 2 6 1 11 2 14
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- Use the following data to estimate the value of a European put option with X = $120. The current stock price now is SO = $100. The two possibilities for ST are $150 and $80. If the risk-free rate is 10%, estimate the value of the put option now. a. P0 = $0 b. P0 = $40 c. P0 = $20.78 d. P0 = $22.86Suppose 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?2. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, = 0.5a. What is correct of the call options using Black-Scholes model? b. Compute the put options price using Black-Scholes model. 3Suppose a European put options has a price higher than that dictated by the putcall parity.a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless.Note: Use the call and put options prices you have computed in the previous question 2 above.b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?
- Suppose you want to price an American style put option for a stock being traded on theDryfontein Stock Exchange having the following parameters: s = 18, t = 0.25, K = 20, σ =0.2 and r = 0.07. Using n = 5, calculate the value of V2(2). Provide all necessary details.1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.77. and put option value is 1.99 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. explainc. What would be the extent of your profit in (a) depend on? explain1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.7739. and put option value is 1.8101 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?
- Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset ... what is the value of the call option? Call Option Price = $4.84 Call Option Price = $2.95 Call Option Price = $7.93 Call Option Price = $12.04Consider 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?How to solve this problem? plz solve it step by step with formulas, thank u! (which one is the risk-free rate? 1% or 2%) Options on Indexes and Currencies Example Suppose that the current exchange rate of AUD to CAD is 1.2 AUD/CAD and o = 0.4463. Find the price of American put option to sell CAD for AUD at K = $1.1 AUD/CAD before or at half a year from now. Assume that the risk-free rates in Canada and Australia are 2% and 1%, respectively. Find the price of the American call option today by using the two period binomial model.
- You buy a put and a call on a stock that expire at time T. They are European options. Both the put and the call have an exercise price of $50. Plot the cash flows at the time of expiry. This strategy has a name. What is it?This question is about futures risk premia. Consider a two period economy.You can buy stocksin period 0, and then sell them in period 1. You can also enter into futures contracts in period 0, whichexpire in period 1. Since buying single-stock futures appears to be a fairly profitable trade, you decide toinvest in a futures strategy. You enter a long futures contract position. You also invest cash in period 0 at the risk-free rate, so you have just enough topay for the futures contract at expiration. You plan to sell the stock just after expiration. What is theexpected return on this trading strategy (in terms of expected period-1 dollars you get, per period-0dollar invested)?Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset … what is the value of the call option?