Arrow prices explorer
Change the states, state prices and payoffs to calculate a security’s price.
An Arrow price is what you pay today for $1 in one particular future state.It pays $0 in every other state. (Lengwiler, 2004, pp. 41–42) Buy the right quantities of these claims to build any payoff below.
See the idea01 / INPUTS
States and payoffs
Enter what your security pays if each state happens.
A default-free bond maturing in one year. One coupon plus principal, paid at the same date in every state.
One unit of a pure Arrow claim; pays $0 otherwise.
| State in one year | Arrow price α$ today per $1 | Probability p% chance | Payoff x$ in that state | α × x$ today | Remove |
|---|
States are mutually exclusive and cover all outcomes. Adding or removing one splits the probabilities equally.
Try this: change a probability, then an Arrow price.
Only the Arrow price changes the price today when payoffs stay fixed.
03 / OUTCOMES
Payoff by realised state
COMPARISON
Arrow prices and bond coupons
The Arrow price is the cost today.
The coupon is a payment in the future.
$1 in just one state
The same coupon in every state
A whole bond also returns its principal. (Lengwiler, 2004, p. 40) Here every payment is one year away; a bond with several coupon dates needs state prices for each payment date.
Where do probabilities fit in?
Actual probability p: how likely you think a state is. It weights the expected future payoff, not the market price directly.
Arrow price α: the market cost today of $1 conditional on that state. It reflects both time and the value of receiving money in that state. If α and payoffs are fixed, changing p alone cannot change the price.
This is a one-period, frictionless pricing model with all listed states feasible and their Arrow claims tradable. Strictly positive state prices are required for no arbitrage in that complete market. (Lengwiler, 2004, p. 49) State prices need not sum to one. (Lengwiler, 2004, pp. 44–45)
Reference
Lengwiler, Y. (2004). Microfoundations of Financial Economics: An Introduction to General Equilibrium Asset Pricing. Princeton University Press. Chapter 3.
Arrow securities and payoff valuation: pp. 41–44. Risk-neutral probabilities and pricing: pp. 44–45. Positive state prices and no arbitrage: p. 49.
The explorer’s coupon example applies the state-price valuation rule to a single payment of principal plus coupon.
Read the author’s freely available book