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梦梦 · 2024年10月03日

关于forward option

  1. FRM I
  2. Financial Markets And Products

NO.PZ2023091802000121

问题如下：

A 1-year forward contract on a stock with a forward price of USD 100 is available for USD 1.50. The table below lists the prices of some barrier options on the same stock with a maturity of 1 year and strike of USD 100. Assuming a continuously compounded risk-free rate of 5% per year what is the price of a European put option on the stock with a strike of USD 100.

Option Price

Up-and-in barrier call, barrier USD 95 USD 5.21

Up-and-out barrier call, barrier USD 95 USD 1.40

Down-and-in barrier put, barrier USD 80 USD 3.5

选项：

A.

USD 2.00

B.

USD 4.90

C.

USD 5.11

D.

USD 6.61

解释：

The sum of the price of up-and-in barrier call and up-and-out barrier call is the price of an otherwise the same European call. The price of the European call is therefore USD 5.21 + USD 1.40 = USD 6.61. The put-call parity relation gives Call – put = Forward (with same strikes and maturities). Thus 6.61 – put = 1.50. Thus put = 6.61 – 1.50 = 5.11

老师，1，“A 1-year forward contract on a stock with a forward price of USD 100 is available for USD 1.50.”这里的100和1.5到底指什么意思，经典题课里说这是forward option，如果是forward option，也是option啊，为什么它的图像和forward一样？


2，barrier usd 95这是什么价格？

3，虽然这道题是same srock，same strik price等等容易误导是用put call parity，但是用put call parity是解不出来的对吗？



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1 个答案

pzqa39 · 2024年10月06日

嗨，努力学习的PZer你好：


1、这个1.5是value，100是price。老师上课讲的是long call+short put可以合成一个远期（涨了赚钱，跌了亏钱）。所以这个图就是合成了一个远期的pay off图。

2、在这个题目中，“barrier USD 95” 指的是 障碍价格，即触发障碍期权激活或失效的价格。

障碍期权是一种特定类型的期权，只有当标的资产的价格在期权有效期内达到或突破某个特定的价格（即障碍价格）时，期权才会被激活或者失效。

对于上破即入障碍看涨期权（up-and-in barrier call），障碍价95美元意味着只有当股票价格在期权到期前达到或超过95美元时，这个看涨期权才会被激活。

对于上破即出障碍看涨期权（up-and-out barrier call），障碍价95美元意味着如果股票价格在期权到期前达到或超过95美元，这个看涨期权会失效。

这两个加起来，可以合成一个没有障碍的看涨期权。

3、是的，这道题用put call parity是解不出来的。

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NO.PZ2023091802000121 问题如下 A 1-yeforwarcontraon a stowith a forwarpriof US100is available for US1.50. The table below lists the prices of some barrieroptions on the same stowith a maturity of 1 yeanstrike of US100.Assuming a continuously compounrisk-free rate of 5% per yewhis thepriof a Europeput option on the stowith a strike of US100. Option PriUp-anin barrier call, barrier US95 US5.21 Up-anout barrier call, barrier US95 US1.40 wn-anin barrier put, barrier US80 US3.5 A.US2.00 B.US4.90 C.US5.11 US6.61 The sum of the priof up-anin barrier call anup-anoutbarrier call is the priof otherwise the same Europecall. The priofthe Europecall is therefore US5.21 + US1.40 = US6.61. The put-callparity relation gives Call – put = Forwar(with same strikes anmaturities).Thus 6.61 – put = 1.50. Thus put = 6.61 – 1.50 = 5.11 有远期合约的put call parity不应该是p+pv(f)=c+pv(x)吗，为什么这道题不需要考虑pv(x)？

2023-10-21 17:12 1 · 回答

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2023-10-18 16:49 1 · 回答