Skip to content
All library documents

Interpreting the Risk-Free Asset as a Bank Deposit

Article Quant Q&A · Author: Morgenman
Read the original

Summary

In a continuous-time pricing model, the risk-free asset grows at a deterministic rate, expressed as a differential equation with interest rate r. The answer interprets this asset as a bank deposit: its value earns interest without a random return component. This explains why the model can describe the asset’s value as changing over time even though the investor initially deposits money into it.

A bond can also be a useful intuition, but the answer points out a modeling mismatch: a conventional bond has a maturity, while the risk-free asset in this setup is treated as having no maturity and continuously paying interest. The discussion is conceptual and does not cover deposit insurance, changing rates, credit risk, or the difference between a model’s idealized risk-free account and actual bank products.

Key ideas

  • The modeled risk-free asset accumulates interest deterministically over time.
  • A bank deposit provides an intuitive interpretation of the asset’s growing value.
  • A conventional bond may not fit the model because it has a maturity date.

Tags

Derivatives pricingFixed income
Full text
# What is the risk-free asset?


# What is the risk-free asset?












We have $dB_t = rB_tdt$.

We are told that this corresponds to a "bank"..... how? When I insert money into a bank, how does this correspond to buying an asset for the price $B_t$?

It would make more sense to say it is a bond, yet my book insists this is a "bank".

## Answer by Stefan Voigt (score 3)

https://quant.stackexchange.com/a/32328

Well, I do not think there is a large difference: Given you deposit money at a Bank the value of this deposit changes according to $$\frac{dB_t}{B_t} = r dt$$ which simply means there is no uncertainty with respect to this evolution (instead of incorporating a risky component $dW_t$. If you really want to interpret the risk-less asset as a bond you are probably faced to some issues (the bond should not exhibit a maturity but instead should only pay interest). Therefore I would agree that it is best to interpret the risk-less term as a bank deposit.

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.