Risk Measures II

Question 1

Implied Delta

Answer 1

• This risk measure is also sensitive to changes in volatility and time (in addition to just price changes in the underlying)
• As vol increases, an OTM call rises and the delta of an ITM call falls, with both tending towards 0
• Rather than try to guess the future volatility, many traders will use the this measure –> the delta that results from using the implied volatility
  ○ Under this approach, the delta will change as implied vol changes, even if the underlying contract remains the same

Question 2

Vanna

Answer 2

the sensitivity of the delta to a change in volatility
-Vanna and volatility are inversely correlated
-Delta values that are already close to 0, 50, or 100 are the least likely to change, while delta vales that are approximately midway between these numbers are the most likely to change

Question 3

Delta Decay or Charm

Answer 3

the sensitivity of the delta to time
-Charm and the passage of time are inversely correlated
Delta values that are already close to 0, 50, or 100 are the least likely to change, while delta vales that are approximately midway between these numbers are the most likely to change

Question 4

Speed

Answer 4

the sensitivity of gamma to a change in the underlying price

Question 5

Color (gamma decay)

Answer 5

the sensitivity of the gamma to the passage of time
○ Color is the greatest for ATM calls and puts
○ Gamma values become smaller as we increase time to exp and larger as we reduce time
○ Color is highest for calls w deltas close to 5 or 95
○ Color is highest for puts w deltas close to -5 or -95
Increase in time causes gamma values to rise, whereas the passage of time causes gamma values to fall

Question 6

Volga (vomma)

Answer 6

the sensitivity of the vega to a change in volatility

Question 7

Vega Decay

Answer 7

the sensitivity of the vega to a change in time

Question 8

Zomma

Answer 8

the sensitivity of the Gamma/Vanna to a change in Volatility/Underlying Price

Question 9

Lambda

Answer 9

Sensitivity of the theoretical value to changes in the underlying price
- The rate of change in percentage terms in relation to the underlying contract
- Lambda is the options delta (using decimal format) multiplied by they ratio of the underlying price (s) to the options theoretical value
○ Lambda = Delta (s/tv)
- Traders will sometimes call lambda the options leverage value
- Calls have positive Lamb
- Puts has neg Lamb
- Lamb is greatest for OTM options
○ As underlying rises, call lamb declines and put lamb increases
○ If vol increases, lamb values for p and c fall
○ Time passes, lamb values for p and c rise
- A trader who wants the highest possible ROI (in percent terms) compared with an equal investment in the underlying contract can maximize his lambda by trading
OTM options close to expiration in a low volatility environment

Question 10

Rhof or Phi

Answer 10

Sensitivity of the theoretical value to changes in the foreign interest rate or dividend yield

Question 11

Theta

Answer 11

• Amount of decay depends on ITM, ATM or OTM
• Theta is greatest when it is ATM
• All else equal, at ATM option at a higher underlying price has a greater theta value than an at the money option with a lower underlying price
  ○ A 1,000 call will be worth more than a 10 call because the 1,000 asset is obv worth more than a 10
• OTM option experiences greater time decay as it approaches expiry than ATM or ITM
• ATM options theta is directly proportional to volatility
  ○ Volatility is proportional to the square root of time
  Theta of ATM option therefore must be proportional to the square root of time

Question 12

Vega

Answer 12

• The vega is greatest when the option is ATM
  ○ Higher vega for higher strike price all else equal (same principle as theta)
• Vanna can also mean the sensitivity of vega to a change in the underlying
• The Vega of an ATM option is constant w respect to changes in volatility
  ○ Whether vol is 20p, 30p, or some higher value, the vega of an ATM option will be the same
• The sensitivity of vega to change in volatility is either volga or vomma
  Vega increases w more time to expiry, and decreases w less time to expiry

*Recall that long term options are always more sensitive to changes in vol than short term options

Question 13

Gamma

Answer 13

• While gamma measures the sensitivity of the delta to a change in the underlying price, gamma itself is sensitive to changes in market conditions
• Gamma is the greatest when the option is ATM
  ○ *gamma, theta, and vega are all the greatest when an option is at the money
  ○ This is why ATM options are the most actively traded
• Gamma of ATM option declines at higher exercise price (UNLIKE theta / vega)
  ○ Gamma is inversely proportional to exercise price. The gamma of an option w an ex price of 50 will be twice as large as the gamma of an option w an ex price of 100
• Sensitivity of gamma to changes in the underlying is called speed
  ○ Speed is highest for OTM calls w deltas close to 15 (puts -15)
  ○ Speed is highest for ITM calls w deltas close to 85 (puts -85)
  ○ Increase time to expiry, speed declines
  ○ Reduce time to expiry, speed rises
  Gamma of ATM option rises as time passes or as we reduce vol; and falls as we increase vol