Python for Finance: Analyze Big Financial Data

Conclusions

This chapter covers some mathematical topics and tools important to finance. For

example, the approximation of functions is important in many financial areas, like yield

curve interpolation and regression-based Monte Carlo valuation approaches for American

options. Convex optimization techniques are also regularly needed in finance; for example,

when calibrating parametric option pricing models to market quotes or implied volatilities

of options.

Numerical integration is, for example, central to the pricing of options and derivatives.

Having derived the risk-neutral probability measure for a (set of) stochastic process(es),

option pricing boils down to taking the expectation of the option’s payoff under the risk-

neutral measure and discounting this value back to the present date. Chapter 10 covers the

simulation of several types of stochastic processes under the risk-neutral measure.

Finally, this chapter introduces symbolic computation with SymPy. For a number of

mathematical operations, like integration, differentiation, or the solving of equations,

symbolic computation can prove a really useful and efficient tool.