# Implied Volatility

## Abstract

In the previous chapters we have used historical data and volatility models for the calculation of volatility. An alternative source of volatility information is contained in implied volatility, which is often referred to as the market’s perception of future volatility over the remaining life of the option. Historical volatility, on the other hand, is a retrospective volatility measure and, provided that the historical data is available, can be calculated for any variable whereas implied volatility is only available for those financial assets on which options are traded. Implied volatility is obtained from option prices in conjuncture with a certain option pricing model. This instantaneous volatility measure is calculated by inserting an implied volatility value in an option pricing formula so that the resulting theoretical value of the option equals its market price. The accuracy of inferred implied volatility therefore not only depends on the efficiency with which the option market subsumes the available information, but also on the use of the correct option pricing model, *i.e*. the model used by the market to price volatility.

## Keywords

Option Price Implied Volatility GARCH Model Underlying Asset Option Market## Preview

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## References

- 1.See Kritzman(1991) for a review on the application of the Newton-Raphson and the bisection method. Also see Brenner and Subrahmanyam (1988) who derive a simple implied volatility formula for the inverted Black-Scholes model which is most accurate for at-the-money options.Google Scholar
- 2.Also see Harvey and Whaley (1992) who show that ad hoc valuation procedures with regard to dividend payments on the Standard and Poor’s 100 index can give rise to large pricing errors. 3Following a large dividend payment the price of the underlying asset, and hence the price of the option, may decrease substantially. Provided that the option is sufficiently in-the-money it might be beneficial to sacrifice the remaining time value of the option.Google Scholar
- 4.See Whaley (1982) who empirically compares several methods for the pricing of American call options on dividend-paying stocks.Google Scholar
- 5.For example, when the price of the underlying assets falls far below the exercise price, the put might prove to be more valuable when exercised immediately as the proceeds can be invested in bonds which will earn a riskless rate.Google Scholar
- 6.An option pricing model which allows for stochastic volatility was introduced by Hull and White (1987).Google Scholar
- 7.See, for example, Rubinstein (1985), Stein (1989), Stein and Stein (1991) and Canina and Figlewski (1993).Google Scholar
- 8.See, for example, Stein (1989) and Xu and Taylor (1994).Google Scholar
- 9.See Whaley (1993) who observes a downward sloping term structure for OEX options with a dramatic increase in implied volatility during their final week of trading. As a possible explanation he suggests that this might be attributable to increased speculation when options are close to maturity.Google Scholar
- 10.The rationale behind using more than one option series is that the noise present in implied volatilities is diversified.Google Scholar
- 11.Also see Whaley (1982) who obtained similar results using a variety of option pricing models, which resulted in approximately the same implied volatility values.Google Scholar
- 12.Although the most sensitive option is usually slightly out-of-the-money Beckers (1981) prefers to refer to this option in his paper as being ”at-the-money”.Google Scholar
- 13.The possible explanations offered by Canina and Figlewski (1993) for their findings are discussed by Christensen and Prabhala (1998).Google Scholar