L15 - Option Sensitivity Flashcards
1
Q
What are the sensitivity factors we consider?
A
- Quantitative factors (from Black-Scholes)
- Underlying Price
- Strike Price
- Volatility
- Time
- Interest rate
- Dividend
- Other factors
- Expectations
- Behavioural finance
2
Q
What are the Greeks?
A
- To estimate the option sensitivity to different factors some synthetic indicators called greeks are used
- the Greeks are quantities representing the sensitivities of derivatives such as the option to change in underlying parameters on which the value of an instrument r portfolio of financial instruments is dependent on
- Also called risk sensitivities, risk measures or hedge parameters
- Each greek measure a different aspect of the risk in an option
- though understanding and managing these greeks, market makers, traders, financial institutions and portfolio managers can mage their risk appropriately
- Each Greek measures the sensitivity of the value of a portfolio to a small change in a is given underlying (using partial derivatives) –> so that components risks may be treated in isolate and the portfolio reblanced accordingly to achieve a desired exposure
3
Q
What are the most common Greeks?
A
- Greeks are the first-orde derivatives
- Delta
- theta
- vega
- Rho
- Second-order derivatives of value –> Gamma
Ther remaining sensitivities are common enough that they have common names, but this list is by no means exhaustive
4
Q
What is Delta?
A
- delta of call options is always positive when the spot price increases
- A call option value will increase by delta for every £1 increase in the underlying
- it has a range from 0 (when OTM) and +1 when deep ITM
- Delta for an ATM option is around 0.5 and decreases when OTM and increases when in the money for a call option
- A call option value will increase by delta for every £1 increase in the underlying
- delta of a put option is always negative when the spot price increases
- ranges from 0 and -1
- A put options value will decrease by delta for every £1 increase in the underlying
- ranges from 0 and -1
-
delta put-call parity
- delta of put = delta of call - 1
- as the sum of the absolute values of the delta is one for the same strike price
5
Q
What is Delta Hedging?
A
6
Q
Example of Delta Hedging?
A
- Take on the opposite position in the underlying of size delta*stocks underlying original option
- In this case for every delta lost in the value of the option, the share price went up by 1*no of shares used for hedging
7
Q
What is the problem with delta hedging?
A
- unfortunately, delta-hedging only works for a short period of time during when the delta of the option is fixed
- The hedge will have to be readjusted periodically to reflect changes in delta, which could be affected by the share price, time to expiry, risk-free rate of return and volatility of the underlying
- Markets may be illiquidity so you cant buy enough stocks to hedge
8
Q
how can Delta be a proxy for probability?
A
- Some options traders also use the absolute value of delta as the probability that the option will expire ITM (if the markets move under Brownian motion)
- For example, if an OTM call option has a delta of 0.15 the trader might estimate that the option has appropriately a 15% chance of expiring ITM
- Similarly, if a put contract has a delta of -0.25 the trader might expect the option to have a 25% probability of expiring ITM.
- ATM options have a delta absolute value of 0.5 so they have a 50% chance of expiring ITM
9
Q
Variations of Delta with Share Price?
A
- Variation of Delta with Time to Expiry (T) for European option on non-dividend paying share with a strike price of X
- the close you get to the expiry date the closer the delta of OTM, ATM and ITM option
- moves closer to the ATM delta –> they are never equal though
10
Q
What is Gamma?
A
- If gamma is small, delta only changes slowly and in order to keep a portfolio (basket of shares and options) delta-neutral adjustments to the portfolio can be made less frequently
- however, if delta is very sensitive and the game is large the portfolio will need to be adjusted more frequently to maintain delta neutrality
11
Q
Example of Gamma?
A
- Only goes till 1 or to 0 wont go any higher or lower
12
Q
Example of using Gamma as a trader?
A
change in delta = (gamma+delta) * no of options bought
13
Q
How can you use Gamma to estimate the market value of your portfolio?
A
14
Q
How does Gamma vary with the share price?
A
15
Q
How does Gamma vary with Time to Expiry?
A
- ITM and OTM options drive gamma towards zero over time
- Because when you are close to the expiry date and you are far from the strike price you know whether the option is in or out
- Gamma increases as the time to expiry decrease for ATM options i.e. the value of the option is highly sensitive to the underlying share price
16
Q
What is Theta?
A
17
Q
How does Theta vary with Time to Expiry?
A
18
Q
How does Theta vary with Time?
A
19
Q
How does Theta vary with share price?
A
20
Q
What is Vega?
A
- Vega is typically expressed as the amount of money, per underlying share the option’s value will gain or lose as volatility rises to falls by 1%
- Vega can be an n important greek to monitor for an option trader especially in volatile markets since some of the value of options strategies can be particularly sensitive to changes in volatility
21
Q
How does Vega vary with strike price?
A
- When you are deep ITM and OTM volatility loses their importance
- Although it holds more significance when you have a long time to expiry
- you may make an OTM into an ITM if it has high enough volatility and time to travel to its price
- However, even with the same volatility an OTM cant move ITM in the space of a day
22
Q
What is Rho?
A
Sometimes use ‘r’ so dont get confused with correlations
23
Q
How does Rho move with the Strike Price?
A
- Interest rates affect an option a lot when its ITM
- this is because it makes the premium more expensive
- as the assumption for option pricing is that we borrow money to by them
