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Introductory Mathematics and Statistics for Islamic Finance, + Website by Noureddine Krichene, Abbas Mirakhor

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Chapter 2Functions and Models

Functions are essential concepts in economics and finance. They describe a relationship between two or more variables. For instance, the quantity of corn produced is a function of acreage, machinery, labor, fertilizers, rainfall, and so on. Each of these variables has a significant effect on the output of corn.

An economic or financial function is called a model. The price of an asset is a function of risk and return. The capital asset pricing model (CAPM) is an example of function that includes risk and return.

The payoff to a futures contract is a function of the futures price and the price of the asset at maturity. The price of a call option is a function of the underlying asset price, the strike price, the volatility of the asset price, the risk-free rate, and maturity.

Practitioners in finance should be able to define a function and present examples of functions in economics and finance. Some of the aspects of functions they should understand include the parametric representation of a function and the notion of vector-valued function. Level curves (i.e., contours) are also important analytical tools in economics and finance.

This chapter shows the application of functions in Islamic finance and the role of functions in describing economic and financial models. In particular, it covers computing the present value of an asset, expected rate of return in the CAPM, forward exchange rates, and payoffs of futures, options, and swaps contracts.

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