A Bramble-esq question.

answer at half past the hour... unless anyone protests.

Hotch I'll PM you the answer if you want to get your beauty sleep
 
I just realised my maths made no sense. 2nd time I've done that today, first time I only notice when I was printing 500 ticks offside...
 
Ok, the option is worth $0.5, so you bid anything up to that.

Why?

Well, we have two scenarios. Either

1), the stock price goes to $101, and the option must then be worth $101 - $100 = $1

2) the stock price goes to $99 and the option expires worthless, $0.

Now the fun bit.

We create a portfolio that gives us a risk free return…

So, we short 1 option, and hold some other quantity, Δ, of the stock.

The portfolio is riskless if we choose Δ such that

($101Δ) - $1 = ($99Δ)

i.e. if we create this portfolio, it doesn’t matter where the stock finishes, we get the same payout.

We solve to give Δ = 0.50

A riskless portfolio is therefore…

Long 0.50 shares
Short 1 option

Then if the stock closes at $101, the portfolio is worth

($101 x 0.5) - $1 = $49.50

and if the stock closes at $99, the portfolio is worth

($99 x 0.50) = $49.50

Now if that portfolio is worth $49.50 tomorrow, what is it worth today? If interest rates are zero, it’s worth $49.50 too…

Now currently the stock price is $100, and we are

Long 0.50 shares
Short 1 option

And this portfolio is worth $49.50. What is the value of the option?

$49.50 = ($100 x 0.50) – Value of Option


The value of the option is therefore $0.5.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Say the value was trading at $0.60, we could Buy 0.50 shares and short 1 option, to give a portfolio value of $49.40 ...

... and irrespective of where the stock price closes, tomorrow it will be worth $49.50!!

No arbitrage means the option trades at $0.50


+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++



The interesting bit here is that the probabilities are not used one bit :)


Neat, eh?
 
Nice.

I assumed the pitfall was in paying for the option and stuf, fundamental lack of knowledge ftw.

Cool beans.

To bed!
 
MrGecko said:
[F the option is worth $0.5, so you bid anything up to that.[/FONT]

[F

[F we have two scenarios. Either[/FONT]

[F the stock price goes to $101, and the option must then be worth $101 - $100 = $1[/FONT]

[F the stock price goes to $99 and the option expires worthless, $0.[/FONT]

[F the fun bit.[/FONT]

[F create a portfolio that gives us a risk free return…[/FONT]

[F we short 1 option, and hold some other quantity, Δ, of the stock.[/FONT]

[F portfolio is riskless if we choose Δ such that[/FONT]

[F ($101Δ) - $1 = ($99Δ)[/FONT]

[F if we create this portfolio, it doesn’t matter where the stock finishes, we get the same payout.[/FONT]

[F solve to give Δ = 0.50[/FONT]

[F riskless portfolio is therefore…[/FONT]

[F Long 0.50 shares[/FONT]
[F Short 1 option[/FONT]

[F if the stock closes at $101, the portfolio is worth[/FONT]

[F ($101 x 0.5) - $1 = $49.50[/FONT]

[F if the stock closes at $99, the portfolio is worth[/FONT]

[F ($99 x 0.50) = $49.50[/FONT]

[F if that portfolio is worth $49.50 tomorrow, what is it worth today? If interest rates are zero, it’s worth $49.50 too…[/FONT]

[F currently the stock price is $100, and we are[/FONT]

[F Long 0.50 shares[/FONT]
[F Short 1 option[/FONT]

[F this portfolio is worth $49.50. What is the value of the option?[/FONT]

[F = ($100 x 0.50) – Value of Option[/FONT]


[F value of the option is therefore $0.5.[/FONT]
++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Say the value was trading at $0.60, we could Buy 0.50 shares and short 1 option, to give a portfolio value of $49.40 ...

... and irrespective of where the stock price closes, tomorrow it will be worth $49.50!!

No arbitrage means the option trades at $0.50


+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++



The interesting bit here is that the probabilities are not used one bit :)


Neat, eh?
Click to expand...

Sorry man you lost me at "Hello".
Just kidding. You must do WAY TOO MUCH THINKING, or are just that smart.
Anyway you look at it hats off to you.

Oh, by the way have you been hanging around the James16 thread over at you know where? Just noticed your avatar. :-0
 
hwsteele said:
Sorry man you lost me at "Hello".
Just kidding. You must do WAY TOO MUCH THINKING, or are just that smart.
Anyway you look at it hats off to you.

Oh, by the way have you been hanging around the James16 thread over at you know where? Just noticed your avatar. :-0
Click to expand...

No, not even a member of FF tbh. Just changed my Avatar 'cos Nine said I was ugly.

For the record, this is elementary stuff, and easy only after someones explained it to you.

You can find explanations of this in any / all derivative textbooks, or just Google the Binomial Model for option pricing.
 
MrGecko said:
No, not even a member of FF tbh. Just changed my Avatar 'cos Nine said I was ugly.

For the record, this is elementary stuff, and easy only after someones explained it to you.

You can find explanations of this in any / all derivative textbooks, or just Google the Binomial Model for option pricing.
Click to expand...

Nine said you are ugly? Now I know why my favorite number is five. How rude.(n)

Elementary stuff? I must be pre-K then. If I can't use the abc's and 123's separately then it's a no-go for me!:eek: Start mixing them together at all and I' m lost.:(
 
Yeah this is exactly delta-hedging, and what traders can do once they sell you an overpriced option to eliminate their risk and lock in profit. Of course you have to include the cost of holding/interest rates in general, but in your case it was only one day. But yeah Gecko, so simple but took years for it to be realised.
 
I was goint to say 10c becasue there's always some fool out there who'll take a stoopid bid...lol
 
Nope, you're confusing what it will cost to hedge the option with what it is rational for you to buy the option for with your superior knowledge of where the stock is going.

It remains rational for you to buy the option at up to 60 cents for exactly the same reason it is rational for you to buy the stock up to $110.20 - you're just trading the stock through the option.
 
But is it rational for you to buy at 59c, when I could take your 59c, use 50c to hedge that option and keep 9c for myself. Why would you rationally give me 9c for free? Surely you would not pay that much, and either pay 50c, or use your money to take up a position in the stock yourself.
 
arabianights said:
Nope, you're confusing what it will cost to hedge the option with what it is rational for you to buy the option for with your superior knowledge of where the stock is going.

It remains rational for you to buy the option at up to 60 cents for exactly the same reason it is rational for you to buy the stock up to $110.20 - you're just trading the stock through the option.
Click to expand...

Is this directed at me?
 
Calinor said:
But is it rational for you to buy at 59c, when I could take your 59c, use 50c to hedge that option and keep 9c for myself. Why would you rationally give me 9c for free? Surely you would not pay that much, and either pay 50c, or use your money to take up a position in the stock yourself.
Click to expand...

It is irrelevant whether you are taking a position in the stock via the outright or the option.

The fair value of the option is 50 cents while the stock remains at $100.

But through your surperior research you know that you have an expected profit bidding the option up to 60 cents or the stock up to $100.20

They are precisely the same thing.
 
If you pay anything other than $0.50 you are creating an arbitrage opportunity for someone else.

The fair price of the option is always [current price of the stock * 0.50] - $49.50

The expectancy of the stock price tomorrow is already included in the price of the stock today, and we are calculating the price of the option today in terms of the stock price. Whatever your model of the probabilities says, they are superfluous to pricing the option.
 
Yes, and if you buy the stock at 100.01 while the market price is 100 then you are also creating an arbitrage opportunity for someone else. That's irrelevant.
 
well plug any option price other than $0.50 into the calculations; there will always be a portfolio you can create that will generate a risk free profit.

Thus the price will converge to $0.50 as the arbitrage opportunities are exploited.
 
TheBramble sure did get a lot of rep from somewhere - literally overnight. One day he had only a little. The next day hes got like 5 stars now. Maybe he has been instructed to lay low for a while so no heat develops (lol) so that when he comes back, nobody notices his yellow star thingies.
 
Last edited:
MrGecko said:
well plug any option price other than $0.50 into the calculations; there will always be a portfolio you can create that will generate a risk free profit.

Thus the price will converge to $0.50 as the arbitrage opportunities are exploited.
Click to expand...

Only if the stock price remains static.

If the option is at 0.50 and the stock is at 100 then you can buy the stock or the option, no difference.

If one is cheaper than the other then the cheaper becomes more attractive, but that will quickly be sorted out by arbitrageurs.

It is still completely rational (in the sense of having +ve expectancy) to bid up to 60 cents for the option and up to 100.20 for the stock.
 
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