CORE I Flashcards
Define gamma.
The gamma is the rate of change in the delta as the underlying price changes. If an option has a gamma of 5, for each point rise (fall) in the price of the underlying, the option will gain (lose) 5 deltas. If the option initially has a delta of 25 and the underlying moves up (down) one full point, the new delta of the option will be 30 (20). If the underlying moves up (down) another point, the new delta will be 35 (15).
What is a general definition of delta?
Measure of an option’s risk with respect to the direction of movement in the underlying contract. The rate of change in the option’s value with respect to movement in the underlying contract.
A call with a delta of 0.25 will change its value at 25% of the rate of change in the price of the underlying. If the underlying rises (falls) 1.00, the option can be expected to rise (fall) 0.25. A call with a delta close to 0.50 will rise or fall in value at just about half the rate of change in the price of the underlying.
If your gamma position is negative,
you want the underlying contract to
sit still or move very slowly.
If your theta position is positive,
the passage of time will…
increase the value of your position.
If your vega position is positive,
you want implied volatility to…
rise.
What is theta?
Theta (time decay) is the rate at which an option loses value as time passes, assuming that all other market conditions remain unchanged. It is usually expressed as value lost per one day’s passage of time. An option with a theta of 0.05 will lose 0.05 in value for each day that passes with no movement in the underlying contract. If its theoretical value today is 4.00, one day later it will be worth 3.95. Two days later it will be worth 3.90.
If your delta position is positive,
you want the underlying price to…
rise.
If your theta position is negative,
the passage of time will…
reduce the value of your position.
Relationship of delta to probability?
Delta is approximately equal to the probability that the option will finish in the money. A call with a delta of 25 or a put with a delta of -25 has approximately a 25% chance of finishing in the money. This also explains why at-the-money options tend to have deltas close to 50. If we assume that price changes are random, there is half a chance that the market will rise (the option goes into the money) and half a chance that the market will fall) the option goes out of the money).
This is only an approximation.
If your gamma position is positive,
you want the underlying contract to…
make big moves or move very quickly.
If your vega position is negative,
you want implied volatility to…
fall.
What is the vega?
Describes the sensitivity of an option’s theoretical value with respect to a change in volatility. Usually expressed as the change in theoretical value for each one percentage point change in volatility. Because all options gain value with rising volatility, the vega for both calls and puts is positive. If an option has a vega of 0.15, for each percentage point increase (decrease) in volatility, the option will gain (lose) 0.15 in theoretical value. If the option has a theoretical value of 3.25 at a volatility of 20%, then it will have a theoretical value of 3.40 at a volatility of 21% and a theoretical value of 3.10 at a volatility of 19%.
If your delta position is negative,
you want the underlying price to…
fall.
An option’s vanna is…
The sensitivity of the delta to a change in volatility.
An option’s charm is…
The sensitivity of the delta to the passage of time.
