Assume that the stock of DiezEight, Inc., is currently trading for $16 and will either rise to $50 or fall to $2 in one year. The risk-free rate for one year is 8 percent. You own a portfolio that consists of one call option and one put option. Both options have a strike price of $15, and both expire in one year. What is the value of your portfolio? (Do not round intermediate computations. Round final answer to two decimal places.)

Question

Quizplus · Accepted Answer

The value of the portfolio consisting of one call and one put option (both with the same strike price and expiration date) can be calculated using the concept of put-call parity, which is given by the formula:$$C + PV(K) = P + S$$Where:- $C$ is the price of the call option,- $PV(K)$ is the present value of the strike price ($K$),- $P$ is the price of the put option, and- $S$ is the current stock price.Given that the strike price ($K$) is $15 and the current stock price ($S$) is $16, and the risk-free rate is 8%, we first calculate the present value of the strike price:$$PV(K) = K / (1 + r) = 15 / (1 + 0.08) = 15 / 1.08 = 13.89$$ (rounded to two decimal places for explanation purposes).The value of the portfolio is the sum of the call and put option prices plus the current stock price minus the present value of the strike price. However, without the individual prices of the call and put options, we directly calculate the value of the portfolio using the stock's potential outcomes.For the call option, the payoff if the stock rises to $50 is $max(0, 50 - 15) = 35$, and if it falls to $2, the payoff is $max(0, 2 - 15) = 0$.For the put option, the payoff if the stock falls to $2 is $max(0, 15 - 2) = 13$, and if it rises to $50, the payoff is $max(0, 15 - 50) = 0$.The expected payoff of the portfolio is the average of the payoffs in both scenarios, discounted back at the risk-free rate:$$Expected\ Payoff = \frac{1}{1 + r} \left(\frac{35 + 13}{2}\right) = \frac{1}{1.08} \left(\frac{48}{2}\right) = \frac{24}{1.08} = 22.22$$However, this calculation does not directly apply to the given options and does not match any of the provided choices, indicating a mistake in the explanation process. The correct approach involves recognizing that the portfolio's value is not directly calculable with the given information without assuming the Black-Scholes model or another option pricing model, which requires more information than provided. The correct answer involves understanding the theoretical framework for pricing such a portfolio, which typically involves complex financial models not fully detailed in the question. Given the error in the explanation, the correct answer should reflect the value of the portfolio under ideal theoretical conditions, but without the exact prices of the call and put options or a detailed model, the precise calculation cannot be accurately completed as attempted. The correct approach would involve using the put-call parity or an option pricing model, which requires inputs not fully provided in the question.

Assume That the Stock of DiezEight, Inc