The One-Period Model

Two States, Two Assets

A one-period model has a risky stock and a risk-free bond.

highlighted = computed this step

Stock states

The stock starts at $100.00 and next period is either $120.00 in the up state or $90.00 in the down state.

S0=$100.00,Su=$120.00,Sd=$90.00S_0=\$100.00,\quad S_u=\$120.00,\quad S_d=\$90.00
One-period stock treeThe stock can move to one of two next-period states.updownTodayS0 $100.00Up stateSu $120.00Down stateSd $90.00

Risk-free bond

The second asset is a risk-free bond: $1.00 today becomes $1.00 next period at 5% interest.

$1.00→$1.00r=5%\$1.00\to \$1.00\quad r=5\%

Model note

This is a one-period, two-state, frictionless model with stated stock states and a single stated risk-free rate. It ignores transaction costs, fees, taxes, credit risk, and liquidity limits. No-arbitrage requires the bond growth to sit strictly between the down and up stock outcomes. This is descriptive, not investment advice.

Sd<(1+r)S0<SuS_d<(1+r)S_0<S_u