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Volatility by Adam S. Iqbal

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CHAPTER 9Black‐Scholes‐Merton Model

The objective in this chapter is to develop a deep and, most importantly, intuitive, understanding of the seminal contributions to option pricing made by Black and Scholes (1973) and Merton (1973). In essence, the BSM approach made mathematical modeling assumptions that allowed the authors to derive a functional form for the option valuation function, namely images.1

Even though it has long been established that real markets deviate substantially from BSM formula, their model still provides the building blocks for the pricing of FX options and valuable insight into how to trade them. For example, we have seen in previous chapters that traders use images in many contexts. Despite the presence of smile directly contradicting the BSM model, traders prefer to perturb the BSM model by making images a function of images, than to discard it.

I split the study of BSM into two parts. This chapter studies the derivation of images and provides its functional form. Until now, we have assumed ...

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