Definition 1 A universe is “risk-neutral” if for all assets A an

Definition 1 A universe is “risk-neutral” if for all assets A and all time periods
t, the value of the asset V (A, 0) at time t = 0 is the expected value of the asset
at time t discounted to its present value using the risk-free rate. The equation
is:
V (A, 0) = e−rtE(V (A, t))


There are many ways to derive the Black-Scholes equation. In this section, we derive it by using
the Capital Asset Pricing Model (CAPM). Let’s begin by reviewing the CAPM, which was
developed primarily by Sharpe (1964), Lintner (1965), and Mossin (1966) and for which Sharpe
was awarded the 1990 Nobel Prize for economics. The CAPM claims that the expected return on
an asset is a linear function of its β , which is defined as the covariance of the return on the asset
with the return on the market, divided by the variance of the return on the market.