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Financial Mathematics by Roman N. Makarov, Giuseppe Campolieti

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Chapter 13

Risk-Neutral Pricing in a Multi-Asset Economy

In the previous chapter we considered continuous-time risk-neutral derivative pricing in the simplest so-called (B, S) economy consisting of only one risky asset (stock) S and a risk-free bond or money market account B. We now extend the (B, S) economy to a continuous-time model of an economy consisting of an arbitrary number n ≥ 1 of tradable risky base assets as well as a money market account. The simplest way to extend the classical (B, S) model to include multiple risky base assets is to assume that they are all independent of one another. For example, we can let each base asset price process be an Itô process, such as a geometric Brownian motion (GBM), driven by an independent Brownian ...

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