Talk:Rational pricing

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Great article. I see you have been doing loads of great work in the option pricing area the last few days Fintor. Thanks very much. Pcb21| Pete 13:45, 11 Jun 2004 (UTC)

I agree, nice article. Just a small question; Why does the definiton of arbitrage state that it requires two (or more) markets? I.e. two assets with similar CF expectations with different price, could be a arbitrage trade with going short in the overpriced and long in the underpriced. Is it my understanding of a market that is unsufficient or the definition? (Cubic)

I think the thing to be careful about is the definition of "market". If I understand you correctly you are saying that in some single market there could be a product trading at two different prices, hence giving rise to an arbitrage opportunity. Well whilst trying to avoid being circular, that is not possible by definition of "market". A market has one price for an instrument. If two different prices are available then that's two markets. (Yep, so a real-life market is not a mathematical "market".)

[edit] Yours!

In this entry it is suggested that:

  • the interest payments of fixed income securities are always known
  • that you should always discount at the government bond yield to maturity

If someone calculates his prices that way, he'll end up way to high. Firstly, the payments are only known in advance for Fixed rate bonds. This only constitutes a part of the bond market. I know, the market is called fixed income, but that's a complete misnomer. If everything were fixed, then there would be very little point in being active in it. Secondly, it is suggested to discount all cash flows at the same government (risk free) discount factor. Unfortunately for most companies, they have to pay more than the government as they are less credit worthy... I.e. their discount factors are much lower. In the current formula: r(t) is too low, so the price is too high (hence: Yours!). Btw - if one wants to use zero coupons, it's better to make the formula C(t) * P(t), instead of C(t) / (1+r(t))^t, i.e. using prices instead of rates, as prices would be more readily available. DocendoDiscimus 00:27, 13 September 2005 (UTC)

Fair comment - what I was suggesting is that
  • iff: the coupons are specified exactly
  • and: there is a zero coupon bond corresponding to each of these
  • then: one can use the "ytm" of the corresponding zcb to discount each coupon/ payment
Should we qualify the wording such that it is clear that (1) this methodology is limited to the above but (2) that the theory applies in general?
Fintor 07:43, 14 September 2005 (UTC)
  • the coupons don't have to be defined exactly for this method to be valid - as long as you then talk about the expected value of each coupon (which you can usually calculate using the yield curve).
  • the most important thing to mention about the zero coupon bond is that it is from the same issuer as the bond we're trying to value. For instance, a zero coupon issued by General Motors would have a much higher YTM than one issued by the US Government.
  • the third point is correct.
I think it's best to say it is always valid, though the zero-coupon bonds are more or less theoretical (considering they depend on the credit of the issuer, and there are very few non-government zero's) -- DocendoDiscimus 12:55, 14 September 2005 (UTC)