SoA6, FE 5.2.6&7, Attainable Cash Flows

[OT]

SoA6
Financial Economics
Exercise 5.8
(Also example in section 5.2.6, page 195, "Suppose that a new security is to be introduced into an existing incomplete securities market model....")

Don’t we need to show that new investment product [0 1 5] in Exercise 5.8 is attainable – especially since we are introducing it into an existing incomplete securities market model?

Similarly, in the example in section 5.2.6, page 195, we price the new investment product, c = [ 1 0 0 1 ], or at least find the range of prices, with out even determining if these cash flows are attainable.

Page 189 also sheds some light on where I am coming from. Here, S(1) * Theta = X. How can we price X (or find the range of prices based on the ranges of Psi) if X can not even be attained from S(1).

Any help or comments would be greatly appreciated.

<font size=-1>[ This Message was edited by: OT on 2002-02-12 23:00 ]</font>

[OT]

Regarding exercise 5.8

We have S(1) =
[
1 30
1 20
1 15
]

and

X =
[
0
1
5
].

Note that there is no theta such that S(1) * theta = X. Since we can not replicate the cash flows, isn’t it a fallacy to calculate a price range (or price) on a cash flow that can not be attained? On the exam could I just stop here by showing that cash flows, X, is not attainable thus excusing me from calculating the price range (or price)?

<font size=-1>[ This Message was edited by: OT on 2002-02-12 23:31 ]</font>

[Axsuetarian]

Hey OT, it looks like you keep posting to yourself!! lol.

Which Jam seminar are you going to?

[Axsuetarian]

Oh, and to answer your question, I think they are adding arrow-debreu securities until they can "span" the marketplace (although I don't think this is explicitly said). The question is "ARE" you even allowed to do that if the market only has said securities in it.. ie - if you can always add "linearly independent" securities to your market, then you can always reach a general equilibrium or "complete" market and then price and derivative or other security using the redundant securities theorem. Maybe this is saying that within this framework of arbitrage pricing theory, we CAN always do this simply because all real world securities exhibit this pricing behavior.

Am I getting too theoretical? Do I have any clue what I am talking about? Boy, Financial Economics is a "light" read :roll:

[Songbird]

I believe your answer lies in page 197.
When you add a redundant security into a complete market, there is exactly one price that makes it arbitrage-free: this is equal to the price of the replicating portfolio.
Here, you are adding an unspanned asset ie an asset not spanned by the existing (incomplete) market. The cashflow of the new instrument cannot be replicated exactly by existing instruments. However, some portfolios have payoffs that DOMINATES the new asset, so they must be priced higher than the new asset, and vice versa, otherwise arbitrage opportunities will arise as "superior" assets are priced lower than "inferior" assets. Thus, the 2 boxes on page 197 let you solve for a RANGE of prices for the new asset that will keep the market arbitrage-free.

[OT]

I think I see it now. We are adding a new security to our model and trying to determine it's price range (in order to avoid arbitrage). This is different than pricing (or finding the price) a derivative security made up of the existing portfolio of available cash flows.

Thanks, all of you. Good luck to you.

<font size=-1>[ This Message was edited by: OT on 2002-02-13 14:01 ]</font>