What is state price vector?.

Please explain me in detail is difficult to understand for me.

  • 1
    $\begingroup$ Where did you hear of this, in what context? What is it that you don't understand? $\endgroup$
    – SRKX
    Nov 25, 2014 at 3:08
  • 1
    $\begingroup$ What means the state price vector, and for that is used? $\endgroup$
    – busterxD
    Nov 25, 2014 at 3:11
  • $\begingroup$ If S_0 is a price vector of N assets in the time zero. If D is a pairce matriz of N assets in n states. If Y is a vector in R^n strictly positive. Then S_0 = DY, why? $\endgroup$
    – busterxD
    Nov 25, 2014 at 3:36
  • 2
    $\begingroup$ Please edit your question and provide all the details - using Latex - there. $\endgroup$
    – Richi Wa
    Dec 2, 2014 at 9:51

1 Answer 1


Based on what I know for a leacture on Arrow Debrue Security assume that we live in a world with only 2 states and a Security $S$

  • State 1 - Inflation > 1%
  • State 2 - Inflation < 1%


  • In State 1 security $ S $ pays 1 i.e the payout fraction is 100%
  • In State 2 security $ S $ pays 0 i.e the payout fraction is 0%

This collection of states and Prices is called state price vector.

If you have more than one Security than you have a state price matrix.

States will such that sum of all payout fractions $ \Sigma_{i=1}^n P_i = 1$. You can treat them as probilities. While pricing a security you can consider all state price vector for $S$ and find the price as $PV(\Sigma_{i=1}^n P_i * S_i^{cf}) $ where $S_i^{cf}$ cashflow from security $S$ in state $i$.

I would recommend you read some papers on it

  • $\begingroup$ Can you also give an interpretation of "state prices"? $\endgroup$
    – emcor
    Nov 25, 2014 at 13:09

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