Macroeconomic Derivatives: I

I am supposed to give a talk for an internal study group at my workplace. I think I'll talk about Robert Shiller's work on macroeconomic derivatives. 

But even though I would love to talk about his work, I am not sure the audience would be too forthcoming. It's going to be a post-lunch talk so not that I have much hope...but unless I have some data / numbers / equations, I am going to loose 'em all (yes, pretty much we are all a little on the nerdy side).

Even before I came across Shiller's book, I had worked on pricing of GDP Indexed Bonds (assisted a friend rather). That should hopefully provide a decent middle ground.

Despite several failed forays, it's an exciting area and something to watch out for in the future. Here is an intro that appeared in one of the issues of NBER digest:

W11929 in the above link refers to one of the most cited survey papers in the area. More later.

Expectations vs. Arbitrage Pricing (Baxter & Rennie): II

Well, as I thought it might be, it was the semantics that was causing the confusion. Still, I think a word is in order on BR's use of the terminology.

BR warn against the use of 'expectations pricing' - a term that they use for pricing using the average of future possible payoffs (justification being the Strong Law of Large Numbers).

I was wrongly interpreting expectations pricing as an alternative term for risk neutral pricing. I may be mistaken but I don't think I have come across this term very frequently, either in texts or in papers - except, of course, in BR. A quick check in Google for the string 'expectation pricing' and 'derivatives' throws up 73 results. Also, if anything, Mark Joshi uses the term expectation pricing interchangably with risk neutral pricing. I didn't check all the links, but most of the other links are seemingly using the term expectations pricing similarly too.

That said, the warning at the outset (the term is first used in Chapter 1, page 2) to th ebeginners to guard against thinking about derivative pricing in the law of large numbers sense is appreciable. The use of the term expectations pricing, however, could have been avoided.

Expectations vs. Arbitrage Pricing (Baxter & Rennie): I

I am told that Baxter and Rennie (BR; Financial Calculus) warns against always starting out with Expectations based pricing by arguing that it assumes the strong law of large numbers to hold - in essence, a statistically motivated argument.

I haven't seen where BR says that (so may be I shouldn't even talking about it), but that to me is quite wrong motivation for favouring no-arbitrage based pricing over expectations based pricing. Expectations based pricing works under the risk-neutral measure, or alternatively, assuming that agents making investment decisions are risk neutral. The reason why it works isn't based on the statistical properties of the stock price process.

Theoretically, of course, the mathematical equivalence between no-arbitrage and existence of a risk-neutral measure always holds. In practice, favouring one over the other would depend on the problem. So, it was rather surprising to come across a statisitcally motivated argument. Since it's claimed to be coming from a source like BR, it's likely I am interpreting it wrongly. Should check it out on my own.