The success of the Black-Scholes (BS) formula is mainly due to the possibility of synthesizing option prices through a unique parameter, the implied volatility, which is so crucial for traders to be directly quoted in many financial markets. This is because the BS formula allows one to immediately convert a volatility into the price at which the related option can be exchanged. The BS model, ho...

A new approach to modelling and pricing derivative securities based on many underlying assets is developed, with the ultimate, practical aim to properly price such derivatives when each underlying shows a volatility smile/skew. We show that the proposed multidimensional model can indeed account for the observed implied volatility smiles for a range of single securities, when each single-asset v...

The unbiasedness tests of implied volatility as a forecast of future realized volatility have found implied volatility to be a biased predictor. We explain this puzzle by recognizing that option prices contain a market risk premium not only on the asset itself, but also on its volatility. We show using a stochastic volatility model, that a call option price can be represented as an expected val...

Several papers have shown that volatility spills over from one stockmarket to another. By concentrating on index options, which depend on forward-looking distributions, this paper is able to take an ex ante approach to spillovers. It asks whether changes in the implied volatility and implied skewness of one market are quickly reflected in other markets, using daily data from the US, Japan and U...

Corridor implied volatility introduced in Carr and Madan (1998) and recently implemented in Andersen and Bondarenko (2007) is obtained from model-free implied volatility by truncating the integration domain between two barriers. Corridor implied volatility is implicitly linked with the concept that the tails of the risk-neutral distribution are estimated with less precision than central values,...

The margin system is a clearinghouse’s first line of defense against the default risk. From the perspectives of a clearinghouse, the utmost concern is to have a prudential system to control the default exposure. Once the level of prudentiality is set, the next concern is the opportunity cost to the investors. It is because high opportunity cost discourages people from hedging futures and thus d...

Estimation of a consistent volatility model of the underlying is crucial for option hedging. The authors illustrate that, compared to the implied/constant volatility method, a local volatility function method can estimate the underlying volatility from option prices more consistently. The result is more accurate hedge parameters and smaller hedging errors. The evidence provided includes an exam...

For general time-dependent local volatility models, we propose new approximation formulas for the price of call options. This extends previous results of [BGM10b] where stochastic expansions combined with Malliavin calculus were performed to obtain approximation formulas based on the local volatility At The Money. Here, we derive alternative expansions involving the local volatility at strike. ...

The implied volatility derived from inverting the Black-Scholes equation to solve for the price of an option is not an unconditional forecast of future volatility (unless volatility is deterministic). It is only a forecast of the square root of the average variance of a biased set of sample paths for the underlying security –those paths that will affect the dynamic hedging of the option. Most r...