What is the convention regarding mtm for collateral

Nonius · Post by **Nonius** » Tue Sep 11, 2012 10:57 pm

Dude. Stop. Really. You may have some exquisitely brilliant thoughts, but a jury of your peers seems to think they are unintelligible. Maybe Aaron understands, or No. 6, but normal people like myself don't. Or something like that.

Cheng · Post by **Cheng** » Wed Sep 12, 2012 9:11 am

Normal people like yourself ? Sure ? Smiley

here · Post by **here** » Wed Sep 12, 2012 1:10 pm

i made several attempts to explain my point and failing BS pricing on W****tt and majority of the people had a similar or even more active presented their disagreement. As I could observed the last time their point at least on my interpretation of the derivatives pricing were more favorable. Hence, for a new-bee it might be a time needed comprehend new point.

Historically the first confuse of the BS pricing was an example. Let we have 2 stocks taking the same values: S ( 0 ) = 2, S ( 1 ) = { 1, 4 } with prob { 0.01, 0.99 } one and { 0.99 , 0.01 } for the second and let K = 2 , r = 0. BS suggests the same call option price C though 1st suggests loss of the premium C with prob 0.99 while the second with the same prob is meaningful.

Later a top professor note that market does not admit such 2 stocks at the same moment. But why it BS pricing make sense in similar situation when lifetime of the 1 stock option is one period and second option is a similar following period.

For people who work as mathematicians such example should raise a question. What is the definition of the BS option price. My subjective point is that there is no formal definition of the call option price and there exists a strategy known as dynamic hedge that defines BS price. The essence of the hedge-pricing is that : buyer of the option states that BS option price is C because borrowing C one can construct a portfolio which can be restructured such that the portfolio will be riskless, ie has a return risk free 'r'.

Note that such underlying idea shows that such defined option price does not look a settlement price between buyer and seller. It looks like a settlement price between borrower bank and lender of the option. These are some original informal thoughts. Formally, BSE derivation has a formal mathematical error. One need some knowledge of stoch calculus which should include the formula integration by parts and some patience to read couple pages

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2140830

silverside · Post by **silverside** » Wed Sep 12, 2012 2:05 pm

sheesh

I was going to say I thought your earlier posts had the makings of a fair point (talking about the relationship between default risk and market risk), but talking about errors in Black Scholes just makes you sound like you can square the circle.

here · Post by **here** » Wed Sep 12, 2012 4:40 pm

I think that mtm collateral is easier to represent for a call option as far as it looks that only seller of the option subjects to default. For example, let we have a random values S ( t j ), j = 0, 1, 2,... n , S ( t 0 ) = x, for call option with given K and t n = T how to present cash flow generated by mtm. Even easier let S ( t j ) takes the same two values with probabilities depending on time. The problem to write mtm cash flow, find its PV and its statistical characteristics. In BS world they omitted risk characteristics of the price. If we will take risk into account it might be one find effect of the risk on pricing even we will use BS approach for spot price

Nonius · Post by **Nonius** » Thu Sep 13, 2012 1:04 am

No, a buyer can default on buying an option under margin calls. I buy an option from you for 1 dollar. Tomorrow i call you for 1 dollar because the price didn't change, the next day the option drops to 50 cents, you call me for 50 cents and I'm Adios motherfucker.

Anyway, ever heard of the John Baez Crackpot Index? We should create the NP Quantpot Index.

here · Post by **here** » Thu Sep 13, 2012 2:33 am

I did not mean margin call. I supposed hypothetical plain vanilla in which at expiration seller of the option default for delivering underlying security for strike price. I do not know whether it is real case or not.

Martinghoul · Post by **Martinghoul** » Thu Sep 13, 2012 8:05 pm

Right, so if you haven't thought about this being a feasible case or not, why are you talking about it? Generally speaking, under what circumstances is this delivery problem possible with the assumption that there's no failed margin calls on the option?

pj · Post by pj » Thu Sep 13, 2012 9:03 pm

Martinghoul,

please keep in mind

When arguing with fools,

don't answer their foolish arguments,

or you will become as foolish as they are

Proverbs 26:4-14

Martinghoul · Post by **Martinghoul** » Thu Sep 13, 2012 9:35 pm

This is an old battle, pj... list and I, we have a history.