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Delta – the sensitivity of the price of an option to a change in spot



• The Delta of an option is a percentage measure of its money- ness, i.e. the likelihood of the option expiring in the money.

• When an option is ATM its Delta is 50%, representing an equal likelihood of the option expiring either In- or Out-The-Money. The Delta of far OTM options approaches 0%. Similarly, options headed increasingly ITM will approach a Delta of 100% of notional as their sensitivity to a change in spot approaches 100%, where for every move in spot the value of the option will change one-to-one; it starts behaving like a Forward.

Gamma – the sensitivity of Delta to a change in spot



• Gamma represents the steepness of Delta: how quickly the option is likely to move from being OTM to ITM (or vice versa).

• Gamma is greatest when an option is ATM, because it is at that point when an option moves ITM or OTM the quickest. In the diagram on the right, Gamma is represented in green (1 month left until expiry) and blue (1 week left until expiry).

Vega – the sensitivity of the price of an option to a change in volatility



• For Vanilla Options, an increase in volatility represents an increase in price. With high volatility – and hence with larger potential spot moves – the likelihood of ending up ITM is greater.

• The graph on the above represents Vega for options with different expiries. We can see that the more time there is to expiry, the greater the sensitivity to volatility.

Theta – the sensitivity of the price of an option to the time remaining until expiry



• Theta is known as time decay, because as time passes the time value of an option decays away (as explained earlier).

• Theta increases as an ATM option approaches expiry, because the closer the expiry event, the more effect the time value has on the option value. The diagram on the left shows this growth as time approaches expiry.

All the Greeks are affected by changes in volatility (vol). As vol rises the uncertainty of where the market rate will be at expiry increases, thus the probability of exercise approaches 50% for all options, and the steepness of Delta diminishes. The Delta of ITM options (with Delta greater than 50%) will decrease, while that of OTM options (Delta less than 50%) will increase.

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