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王楚溪 · 2021年08月23日

老师您好，请问这里的51.5 cash inflow 是怎么算的？

  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.

是strike price加dividend吗？为什么是这两个数相加啊？

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李坏_品职助教 · 2021年08月24日

嗨，努力学习的PZer你好：


51.5是期初short stock（做空股票，得到现金）得到的54，减去buy call option（题干给出的call option is selling for 2.5 USD）付出的2.5。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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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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