3. A Consider two portfolios: Portfolio A consists of one European call option plus an zero which pays K at time T; Portfolio B consists of one European put option plus a share of the underlying stock. The stock pays no dividend. Both options have the same underlying stock, the same expiration date T and the strike price K. Graph the time-T value of both portfolios (in separate pictures) as functions of the stock price S = S(T).
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- In the Black-Scholes option pricing model, the value of a call is inversely related to: a. the risk-free interest stock b. the volatility of the stock c. its time to expiration date d. its stock price e. its strike priceLet 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 ?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.
- 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.Refer to the graph below, what is the beta of portfolio X under CAPM? E(r) A 0.14 0.10 0.06 N Beta of portfolio X = place) M X o(r) (to the nearest 1 decimalConsider a stock that pays no dividends on which a futurescontract, a call option, and a put option trade. The maturity date for all three contracts is T, the strikeprice of both the put and the call is K, and the futures price is F. Prove that if K = F, then the price ofthe call option equals the price of the put option.
- 4. Valuation of a Derivative Consider a derivative on a stock with the time to expiration T and the following payoff: 0 K₁ 0 if ST K₁. What is the present value of the derivative? Provide an analytic expression of the price using N(), the cumulative probability distribution function of a standard normal random variable.Consider a stock that pays no dividends on which a futures contract, a call option, and a put option trade. The maturity date for all three contracts is T, the exercise price of both the put and the call is X, and the futures price is F. Show that if X = F, then the call price equals the put price. Use parity conditions to guide your demonstration.Please choose on the options and please explain
- Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rf. The characteristics of two of the stocks are as follows: Correlation = -1 Stock Rate of return B O Yes ● No Expected Return Required: a. Calculate the expected rate of return on this risk-free portfolio? (Hint: Can a particular stock portfolio be formed to create a "synthetic" risk-free asset?) (Round your answer to 2 decimal places.) % 6% 12% Standard Deviation 25% 75% b. Could the equilibrium rf be greater than rate of return?Question: There are three securities in the market. The following chart shows their possible payoffs: &n... Edit question There are three securities in the market. The following chart shows their possible payoffs: State Probabilityof Outcome Return on Security 1 Return on Security 2 Return on Security 3 1 .14 .199 .199 .049 2 .36 .149 .099 .099 3 .36 .099 .149 .149 4 .14 .049 .049 .199 a-1. What is the expected return of each security? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Answer 12.40% a-2. What is the standard deviation of each security? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Answer 4.50% b-1. What are the covariances between the pairs of securities? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your…You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio X Y Z Market Risk-free Rp 14.0% 13.0 .8.5 12.0 7.2 Ор 39.00% 34.00 24.00 29.00 0 Bp 1.50 1.15 0.90 1.00 0 Assume that the correlation of returns on Portfolio Y to returns on the market is 0.90. What percentage of Portfolio Y's return is driven by the market? Note: Enter your answer as a decimal not a percentage. Round your answer to 4 decimal places. R-squared