Abstract
The main measures of vanilla option market risk are sometimes referred to collectively as ‘the Greeks’. Numerous texts are available that provide closed form solutions for these metrics, for example, Haug (2007).
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Notes
- 1.
Strictly speaking the underlying price for a European-style option is a forward price with the same time to maturity as the option. However, anecdotally the author has seen many equity option practitioners refer casually to the spot price as the underlying price. Arguably it would be more accurate to refer to the ‘moneyness’ of the option in relation to the forward (ATMF) or relative to the spot price (ATMS).
- 2.
It is an urban myth to say that all ATM options always have a delta of exactly 50 %.
- 3.
This calculation does assume that one option references one underlying asset so if each option references, say, 100 shares, the delta equivalent would be 100,000 options × 100 shares × 54.86 % = 5,486,000 shares.
- 4.
Indeed, it is possible to derive Greek measures that consider how gamma changes with respect to changes in implied volatility (‘zomma’), the spot price (‘speed’) and the passage of time (‘colour’).
- 5.
The option in this trading example is struck ATM spot rather than ATM forward which is used elsewhere in the chapter.
- 6.
Vega is an option’s exposure to a change in implied volatility. See Sect. 5.6.
- 7.
Sometimes the process of trading options and delta hedging frequently is referred to as ‘gamma scalping’.
- 8.
The relationship between the level of the cash market and implied volatility will be considered in Chap. 6. In general terms the relationship tends to be inverse but like all things in finance there are always exceptions.
- 9.
The trader may also delta hedge such a position as both of these options as described would be delta negative.
Bibliography
Haug, E. (2007) The complete guide to option pricing formulas McGraw Hill
Hull, J.C. (2012) Options, futures and other derivatives Pearson
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Schofield, N.C. (2017). Risk Management of Vanilla Equity Options. In: Equity Derivatives. Palgrave Macmillan, London. https://doi.org/10.1057/978-0-230-39107-9_5
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DOI: https://doi.org/10.1057/978-0-230-39107-9_5
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