- Risky Assets 71
normal distribution.Thenumberσis called thevolatilityof the priceS(t). The
density of the distribution ofS(t) is shown in Figure 3.11 fort= 10,S(0) = 1,
m=0andσ=0.1. This can be compared with the discrete distribution in
Figure 3.2.
Remark 3.6
Equation (3.9) and the increments dS(t), dW(t)anddtare introduced above
only informally by analogy with the discrete case. They can be given a pre-
cise status inStochastic Calculus, a theory with fundamental applications in
advanced mathematical finance. In particular, (3.9) is an example of what is
known as astochastic differential equation.