State Price Vectors and Pricing Cash Flows Across States

Summary

The document introduces a state price vector through a two-state example: inflation is either above or below a threshold, and a security pays in one state but not the other. It describes the collection of state-contingent prices as a vector, and says multiple securities can be represented with a state price matrix. The intended use is to combine state prices with a security’s cash flows to derive a present value.

The explanation is brief and informal, and its notation is imprecise: state prices are generally prices today of claims paying in a particular state, rather than probabilities. They can be used to price a payoff by summing each state-contingent payoff times its state price, with discounting conventions handled consistently. The post’s claim that the entries sum to one and can be treated as probabilities is not generally valid without additional assumptions or normalization, so readers should distinguish state prices from probabilities.

Key ideas

• A state price is associated with a payoff contingent on a particular state.
• A payoff can be valued by weighting its state-contingent cash flows by state prices.
• Multiple securities and states can be organized in a matrix of payoffs or prices.
• State prices are not generally probabilities and need not sum to one.

Tags

# What's state price vector?


# What's state price vector?












What is state price vector?.

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

## Answer by ash (score 1)

https://quant.stackexchange.com/a/15619

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%

And

- 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

- Arrow Debreu Prices

- Wikipedia

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.