Market Risk (Equities, FX, Commodities)

This chapter introduces the no-arbitrage models for pricing market risk, assuming that default-free interest rates are non-random. This constant interest rate assumption restricts the model’s use to assets that are shortdated and whose price movements are uncorrelated to interest rates. Hence, the qualification in the chapter title to equities, foreign currencies (FX), and commodities. For real applications, since interest rates are stochastic, the assumption of constant interest rates needs to be relaxed. This will be done in the next chapter.Historically, the no-arbitrage approach for pricing assets under constant interest rates was first presented by Black Scholes Merton (BSM) [5], [52] in the context of a very simple evolution for the risky asset price process, called geometric Brownian motion. For the purposes of this chapter, although we maintain the constant interest rate assumption, we generalize the evolution of the asset price process. Because the model presented here is based on the original BSM paper, we call it the BSM methodology.