I have been working on the question below and I'm stuck on how to finish it up.  I have provided what I've done so far.  Is what I've done so far correct?  And how do I finish up the problem? Here is the question: Suppose that C is the price of a European call option to purchase a security whose present price is S. Show that if C>S then there is an opportunity for arbitrage (i.e. risk-less profit). You may assume the interest rate is r=0 so that the present value calculations are unnecessary. My work so far: There is an opportunity for arbitrage if we can create a portfolio that initially (time t=0) generates a zero net cash flow or a cash inflow, but still produce a positive or zero cash inflow at the time of expiration. Assume we are going to short sell one call option C, and buy one stock S. Consider the cash flows at time t=0.Cash flow of selling one call option: +CCash flow of buying one stock: -STherefore, since C>S, we have an initial cash inflow of C-S>0. We will now consider the value at the time of expiration. (This is where I get stuck.  Any advice/corrections are greatly appreciated.  Thanks!)

Question

I have been working on the question below and I'm stuck on how to finish it up.  I have provided what I've done so far.  Is what I've done so far correct?  And how do I finish up the problem?

Here is the question:

Suppose that C is the price of a European call option to purchase a security whose present price is S. Show that if C>S then there is an opportunity for arbitrage (i.e. risk-less profit). You may assume the interest rate is r=0 so that the present value calculations are unnecessary.

My work so far:

There is an opportunity for arbitrage if we can create a portfolio that initially (time t=0) generates a zero net cash flow or a cash inflow, but still produce a positive or zero cash inflow at the time of expiration.

Assume we are going to short sell one call option C, and buy one stock S.

Consider the cash flows at time t=0.
Cash flow of selling one call option: +C
Cash flow of buying one stock: -S
Therefore, since C>S, we have an initial cash inflow of C-S>0.

We will now consider the value at the time of expiration.

(This is where I get stuck.  Any advice/corrections are greatly appreciated.  Thanks!)

 

 

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