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nanaluo · 2021年10月17日

请问这道题的操作过程怎么理解？

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021203000072

问题如下：

A four-month European call option on a stock is currently selling for USD 2.50. The current stock price is USD 54, and the strike price is USD 50. A dividend of USD 1.50 is expected in one month. The risk-free interest rate is 3% per annum (annually compounded) for all maturities. What opportunities are there for an arbitrageur?

选项：

解释：

The lower bound for the option price is

S−PV(K)−PV(Divs)=54−501.031/3−1.51.031/12=2.99S-PV(K)-PV(Divs)=54-\frac{50}{1.03^{1/3}}-\frac{1.5}{1.03^{1/12}}=2.99

The option is selling for less than its lower bound. An arbitrageur can buy the option and short the stock for an initial cash inflow of USD 51.50. The arbitrageur has to pay dividends of USD 1.50 after one month.

If the option is exercised, the cost of closing out the short position will be USO 50. If it is not exercised, the cost of closing out the short position will be less than USD 50. The worst-case scenario for the arbitrageur is therefore:

Today: +51.50,

One month: -1.50, and

Four months: -50.00.

When the discount rate is zero, the sum of these cash flows will have zero present value. Any positive discount rate gives a positive sum of present values.

请问这道题的操作过程怎么理解？

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品职答疑小助手雍 · 2021年10月18日

同学你好，算出来option是低估的，那期初就是花2.5买这个call，借这个股票卖出获得54元，净现金流是流入51.5元，投资risk free。

过了一个月，借的股票要给别人1.5元，净流出1.5元。


第四个月末，如果股价X不到50元，期权不行权，花X买回股票归还给借出方，净现金是流出X，这种情况下收益是51.5-1.5-X=50-X，X小于50，所以是盈利的；

如果股价X超过50元，期权行权，花50元买股票，归还给借出方，净现金流出是50，这种情况下收益是51.5-1.5-50=0元，期间赚了拿51.5投risk free的收益。


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NO.PZ2020021203000072问题如下A four-month Europecall option on a stois currently selling for US2.50. The current stopriis US54, anthe strike priis US50. A vinof US1.50 is expectein one month. The risk-free interest rate is 3% per annum (annually compoun for all maturities. Whopportunities are there for arbitrageur? The lower bounfor the option priisS−PV(K)−PV(vs)=54−501.031/3−1.51.031/12=2.99S-PV(K)-PV(vs)=54-\frac{50}{1.03^{1/3}}-\frac{1.5}{1.03^{1/12}}=2.99S−PV(K)−PV(vs)=54−1.031/350​−1.031/121.5​=2.99The option is selling for less thits lower boun arbitrageur cbuy the option anshort the stofor initicash inflow of US51.50. The arbitrageur hto pvin of US1.50 after one month.If the option is exercise the cost of closing out the short position will USO 50. If it is not exercise the cost of closing out the short position will less thUS50. The worst-case scenario for the arbitrageur is therefore:Toy: +51.50,One month: -1.50, anour months: -50.00.When the scount rate is zero, the sum of these cash flows will have zero present value. Any positive scount rate gives a positive sum of present values.If option is exercise the cost of closing short position is 50是什么意思啊

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