Consider a stock priced at $150 that can either increase to $200 or decrease to $100 in one year. To price a European put option on this stock expiring in one year using a replicating portfolio, you would need to:

Question

BlackTom AI · Accepted Answer

The question describes pricing a European put option on a stock in one period using a replicating portfolio in a binomial model, where the stock can move to S_u = 200 or S_d = 100 from S0 = 150. We are asked to evaluate the given options for how to construct the replicating portfolio.
Option A: Buy the underlying stock. This would create exposure to the stock’s upside and downside movements directly. However, a put payoff is (K − S_T)^+ and in a one-period binomial model, the put’s value is replicated by combining a position in the stock and a risk-free asset. Merely buying the stock does not capture the required payoff pattern of a put across both possible future states. Therefore this choice does not replicate the put payoff and is not appropriate for the replication strategy.
Option B: You do not need to buy or sell the underlying stock. In a standard one-period binomial replication for options, especially for a put, the payoff in each future state depends on the stock price, and a combination of stock and cash is typically required to match the payoff in both states. Claiming no position in the stock is sufficient ignores the dependence of the put payoff on S_T and fails to replicate the payoff structure across both states. This makes the option incorrect.
Option C: Short the underlying stock. In many one-period binomial replication problems for puts, the delta (the number of shares of stock to hold) is chosen so that the portfolio’s value matches the put’s payoffs in both up and down states. Depending on the strike and the state prices, the replicating portfolio can involve a short position in the stock (negative delta) combined with a position in the risk-free asset to hedge the other state. Since the stock’s up and down movements affect the put payoff asymmetrically, having a short stock component is often necessary to match the required payoffs in both possible future states, making this option consistent with standard replication logic for puts in a binomial model.
Conclusion-driven intuition (without stating it outright): Among the offered choices, selecting a strategy that includes selling (shorting) the stock aligns with the need to offset the stock’s price changes to replicate the put’s non-linear payoff across the up and down states. This makes Option C the correct structure in the typical one-period binomial replication setup for a put.

BU.232.710.F1.SP25 Quiz #2- Requires Respondus LockDown Browser

Consider a stock priced at $150 that can either increase to $200 or decrease to $100 in one year. To price a European put option on this stock expiring in one year using a replicating portfolio, you would need to:

查看解析

登录即可查看完整答案

类似问题

Select all of the statements below that are TRUE.

When the non-dividend paying stock price is $30, the strike price is $29, the risk-free rate is 4% with continuous compounding, the volatility is 20% and the time to maturity is 6 months which of the following is the price of a European put option on the stock?

When the Black-Scholes-Merton and binomial tree models are used to value an option on a non-dividend-paying stock, which of the following is true?

It is the days after the Supreme Court rules tariffs are illegal. Markets are rallying. SPX = 6000 K = 5900 t = 3 months (0.25) r = 4.5% Implied Volatility = 25% The value of the call option is closest to:

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单