Bank account

In a discrete-time market, the bank account reinvests at each successive spot interest rate:

B_{0} = 1, B_{t} = \prod_{s = 0}^{t - 1} (1 + r_{s}) .

(1)

Table of contents
- Rolling one-period bond account Bank account
- Continuous-time bank account Bank account

Rolling one-period bond account ( $β_{t} = β_{t - 1} / P_{t - 1} (t)$ )

 0  0

Reinvest each maturity payment in the next unit-principal zero-coupon bond. Positive bond prices make the resulting self-financing portfolio strictly positive, so it can be used as a numéraire. Its one-step growth is the reciprocal of the current one-period bond price.