During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

We document a surprising pattern in S&P 500 option prices. When implied volatilities are
graphed against a standard measure of moneyness, the implied volatility smirk does not …

Given the price of a call or put option, the Black-Scholes implied volatility is the unique
volatility parameter for which the Black-Scholes formula recovers the option price. This …

The prices of index options at a given date are usually represented via the corresponding
implied volatility surface, presenting skew/smile features and term structure which several …

Consider options on a nonnegative underlying random variable with arbitrary distribution. In
the absence of arbitrage, we show that at any maturity T, the large‐strike tail of the Black …

We develop a new option pricing framework that tightly integrates with how institutional
investors manage options positions. The framework starts with the near-term dynamics of the …

The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of
20th century finance, and remains the most widely applied theory in all of finance. Despite …

This paper describes a method of extracting the risk-neutral probability distribution of future
exchange rates from option prices. In foreign exchange markets interbank option pricing …

Using nine years of options data, we reconstruct a time-series for the at-the-money implied
volatility skew of the SP500 index, and analyse its term structure. Though the well-known …

This paper develops a new top‐down valuation framework that links the pricing of an option
investment to its daily profit and loss attribution. The framework uses the Black‐Merton …