Abstract
Volatility is the annualized standard deviation of the log of the daily return of a stock or index price, whereas variance is the square of the standard deviation. However, this particular definition of volatility is sometimes referred to as ‘realized’ or ‘historical’, that is, it is a backward-looking measure that captures the magnitude of historical price movements. Implied volatility is a forward-looking measure of volatility—it is attempting to capture what the market expects the asset’s actual volatility to be over some future time period.
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Notes
- 1.
This may be shortened sometimes to ‘0.3/0.5 puts over’.
- 2.
See Schofield and Bowler (2011).
- 3.
The appendix to Chap. 6 shows the ‘traditional’ method of calculating a standard deviation (i.e. realized volatility).
- 4.
Carry is assumed to be zero so spot and forward are identical.
- 5.
The trading is assumed to be intraday and so there is no theta effect.
- 6.
The implied volatility used to price the option was 20 % per annum. Since the option’s maturity was 3 months this is scaled by dividing by the square root of the number of 3-month trading periods in a year, that is, the square root of 4 which is 2. Hence 20 % divided by 2 is 10 %.
- 7.
The dollar delta is the ‘delta equivalent’ value of the option, that is, notional × delta. The dollar gamma is the change in the dollar delta for a 1 % move in the underlying.
Bibliography
BNP Paribas (2007) Corridor variance swaps BNP Paribas research
Brask, A. (2004) Variance swap primer Barclays Capital Research
Brask, A. (2005) Forward variance swap primer Barclays Capital Research
De Weert, F. (2008) Exotic option trading Wiley
Schofield, N.C., & Bowler, T. (2011) Trading, the fixed income, inflation and credit markets: a relative value guide Wiley Finance Series
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Schofield, N.C. (2017). Trading Volatility. In: Equity Derivatives. Palgrave Macmillan, London. https://doi.org/10.1057/978-0-230-39107-9_14
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DOI: https://doi.org/10.1057/978-0-230-39107-9_14
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