Iqbal, Volatility

Adam S. Iqbal is the global head of FX Exotics and Correlation at Goldman Sachs and was formerly an FX options trader and portfolio manager at Barclays and Pimco. He holds a Ph.D. in financial mathematics and financial economics.

In Volatility: Practical Options Theory (Wiley, 2018) Iqbal sets himself the goal of providing “an intuitive, as well as technical, understanding of both the basic and advanced ideas in options theory, with the aim of encouraging translational work from theory into practical application by market makers, portfolio managers, investment managers, risk managers, traders, and other market practitioners.” Only peripherally is he writing for the retail options trader with a mathematical bent. He draws his examples from the FX market.

The ability to delta hedge, Iqbal explains, means that “options are fundamentally not bets on direction, but are bets on volatility.” Moreover, the spot FX rate is a martingale, so it exhibits no mean reversion or autocorrelation. Price-based predictability therefore has no place in probability distributions used to model FX rates for the purpose of option pricing.

What matters, and what professionals who use and price options should understand before they embark on building models or, under time constraints, in lieu of relying on models, are the major principles underlying options—first- and second-order greeks as well as implied volatility and term structure (along with smile and skewness). Only after all of these concepts are described in detail does Iqbal introduce the Black-Scholes-Merton model.

Iqbal provides examples of how the trader might make decisions without invoking a full-fledged mathematical model. In the case of a risk reversal, for instance, “one way that traders use to circumvent disagreements over volatility references is to trade a contract known as a risk reversal by smile vega. The idea here is that, since the seller of the risk reversal believes in lower volatility references, if she agrees to trade at the higher volatility references, she can sell a higher notional of the put than she purchases of the call.”

Or take the case in which a normal distribution is priced into options but market participants begin to realize that the actual distribution is leptokurtic, with a higher peak and fatter tales. The peak “means that spot is more likely to remain in the center of the distribution than is currently priced. This means that they sell ATM straddles to profit from the additional probability that we observe only very small moves. Second, they realize that spot is also more likely to exhibit a very large positive or negative return than is priced. They therefore look to purchase OTM strangles. That is, market participants buy the butterfly. … [T]he more kurtosis there is in the spot PDF, the higher the fair price should be for the butterfly.”