I think BearXu still has a point here:
Paul>> That actually looks like the payoff of a long call position and a long
cash position. There's nothing that says the investor has to put the
cash they didn't use to buy the stock when they opened the call position
into cash.
Although this is true, investing in other assets would only affect the size of r in [110+r-(90+C)]$ but not the question if r is to be included or not which is BearXu's main concern.
Paul>> The investor could have taken out the option position C without having
cash to buy the stock ever.
This is also not so important since it would simply introduce opportunity costs on the side of the stock buyer or, which would be the same, savings of opportunity costs on the side of the call buyer which leads back to [110+r-(90+C)]$.
-----Original Message-----
From: r-sig-finance-bounces@stat.math.ethz.ch on behalf of Paul DeBruicker
Sent: Tue 5/12/2009 8:57 PM
To: BearXu
Cc: r-sig-finance@stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] the payoff of an call option
BearXu wrote:
> A more detail example.
>
> If there are two persons: A and B, A wants to buy a stock; B wants to buy an
> option of this stock and the strike price of it is 90$.Now they both have
> 100$. Suppose the stock price now is 100$.
>
> So A use his 100$ buy a stock, and B use a little money C <100$ buy an
> option and save other money into bank.
>
> One year later, the stock price is 110$, so the profit of A is [110-100]$
> and B took his money out from the bank 90$ to buy the stock and his profit
> from this trade is [110-(90+C)]$, but he still got another profit from the
> bank interests during the time because he saved the money in it. So his
> total profit is [110+r-(90+C)]$.
>
>
There are no margin requirements for buying call options.
The investor could have taken out the option position C without having
cash to buy the stock ever. If you exercise and sell at expiration all
the cash you ever need is the premium paid at initiation. The
settlement dates on the transactions can be the same so you wouldn't
have to borrow the cash to exercise. And really, in most cases you
wouldn't exercise, you'd just sell it back.
Regardless, I'm not sure what any of this has to do with the
intersection of R and Finance.
Paul
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