In this chapter, we continue the discussion of the option Greeks that we began in Chapter 5, where we looked at delta. Although it is possible to consider each of the Greeks quantitatively, it is also important to understand intuitively how they operate; to do so we need to describe first the concept of implied volatility.

Volatility has a central role to play in options pricing. In the Black–Scholes framework, volatility is the only input that is not directly observable (as opposed to the price of the underlying asset or the level of the interest rate) but its role is crucial since an over- or underestimation of the actual volatility relative to the implied volatility during the life of the option may have serious consequences in terms of the profit and loss of the options replication via the delta-hedging process or trading in the underlying to replicate the option. So far we have not been very clear on how an option trader will arrive at the volatility input. In some cases, it will be estimated from historical data. In other cases, it may simply be an exogenous input.^{1}

In this chapter, we will shed some light on volatility and its significance in the options markets. At the end of this chapter we will show an example of the behaviour of the implied volatility of the EUR/USD FX rate and the S&P 500 Index based on real data.

Before proceeding, let us start from a very simple (and unrealistic but useful) example. Assume, ...

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