Topic 9: Volatility and Complex Strategies Flashcards
Define VEGA
VEGA: sensitivity of option value to change in volatility of underlying asset
Define GAMMA
GAMMA: second-order derivative wrt underlying asset value
Define THETA
Time
Differences between Vega and Volatility
- VEGA: holds all variable OTHER THAN VOLATILITY constant while correlation In volatility do not hold other variables constant
- Long equity = ZERO Vega but short vol since higher vol means lower return. Therefore delta is one.
- Deep in the money equity calls have positive Vega, but negative vol
Examples of asset classes with short volatility
Since VIX futures are positively correlated with equity market vol and tend to decline in value due to negative risk premium, if you long VIX contracts, you enjoy the hedging benefit of negative equity betas but pay for protection.
EXPECTED returns less than riskless rate
- write option
- long traditional equity
Key reasons Implied Vol differ for options with same underlying but different strikes or tenors:
- Skewness and Kurtosis
- Time varying vol
- Autocorrelation
- Time varying risk premiume
Implied Vol of OUT OF THE MONEY put is ____ than the implied vol of AT THE MONEY put
Implied Vol of OUT OF THE MONEY put is HIGHER than the implied vol of AT THE MONEY put
According to Nossman and Wilhelmsson, the positive risk premium of short volatility products compensates sellers for ___
The compensation (i.e., positive risk premium or expected return) associated with short volatility positions is for two volatility risk premiums:
- volatility diffusion (continuous accrual of small changes in volatility)
- volatility jump (large, sudden increase in volatility) risk.
What pattern does realised return volatility follow
Discrete
For convertible bonds, what is gamma a measure of?
Gamma is the second partial derivative of the convertible bond price with respect to the stock price and, therefore, is a measure of the curvature of the relationship between the convertible bond price and its underlying stock price.
Which options have the highest implied vol?
Deep out of the money
Reasons why volatility strategies have recovered from drawdowns quickly (i.e., in less than one year)
- Periods of high volatility are short due to the high degree of mean reversion in realized volatility.
- After a crisis, there is a greater demand for long volatility products by investors in traditional assets.
What is the economic rationale proving that implied vol of SPY options exceed realised volatility over the long term?
Investors with short volatility positions should earn a consistent profit (i.e., returns greater than the riskless rate) from exposure to the volatility factor.
The consistent profit to short option positions comes from implied volatility consistently exceeding realized volatility.
Volatility derivatives are:
1. ___ vol
2. ___ market risk
3. carry ___ risk premium
Volatility derivatives are:
1. long vol
2. short market risk
3. carry negative risk premium
In a volatility skew, which types of options have higher IVs
ATM puts have lower IVs than Out of The Money and In The Money options
Which has higher IV? Out of the money PUTS or CALLS?
Puts
Rank the ones with highest to lowest IVs
ATM
ITM
OTM puts
OTM put –> ATM put –> ITM put
When is GAMMA the highest and lowest?
Highest: near the money option
Lowest: in/out of the money option
How to execute dispersion trade?
Sell index options
Buy options on the index components
Option positions all hedged to be delta neutral
When does delta portfolio make money?
When underlying stock’s ____ volatility is less than the PUT’s ____ volatility
When underlying stock’s REALISED volatility is less than the PUT’s IMPLIED volatility
Define Knighting uncertainty
cannot form reasonable quantified estimates of either outcomes or possibilities
Name the 5 mortality rate factors according to Krutov (2010)
- Cat events
- Fluctations
- incorrect estimations of trends
- Miscalculations of claims
- Data issues
Is complexity a return factor
No, evidence is not conclusive
What are lock boxes?
Bank accounts for asset backed lenders to receive account receivables
Name the 4 internal credit enhancements
- senior/sub certs
- overcollateralisation
- excess spread
- spread accounts (if performance indicators fall below threshold, any excess spread is put into account to benefit note holders)
Name the 3 external credit enhancements
- cash collateral accounts
- third party letters of credit
- collateral invested amounts
What is a ticking fee
Fee paid to lenders by borrowers to compensate for time lag between loan commitment and disbursement
Differences between warrants and equity options
- Warrant maturities are longer
- Warrants issued by unlisted firms
- Not standardised securitites
- Dilutive then issued by firm
What does it mean by price is sticky?
Price stickiness refers to prices being slow to respond to changes in economic conditions.
The law of one price implies that prices denominated in different currencies should quickly adjust to changes in exchange rates.
If the law of one price holds (which requires perfect markets with no arbitrage costs), then hedging currency risk is not necessary.
Define a quanto option
An option whose payoff is determined in a different currency based on pre-determined exchange rate
Investment Property forum study found that median transaction times fro sale of real estate properties are affected by:
- State of market
- Building location and quality
- Method of sale
- Type of real estate
- Type of buyer and seller
NOT important
1. Asset price
2. Brokerage
Observations about realised volatility (Sinclair 2013)
- mean reverts
- typically low, then increases and remains at higher for some time
- ST can be high; LR reverts to mean
- high vol = increased risk aversion = negatively related to risky asset return
- high vol = bad price
- vol faster in bear market than bull
what is volatility clustering
large changes tend to be followed by large changes, small then small
key differences between long vol and tail risk funds
- long vol uses less aggressive strategies
- vary vol exposure and hold more asset spread position than tail risk funds (do not need to provide protection at all times)
Advantages of complex products
- Complete the market
- Enable investors to earn postive complexity risk premium
Define recourse loan
Allows lenders to seize borrowers’ assets beyond loan collateral to collect amount owed
Define indemnity based longevity swap
Pension plan making periodic fixed payments to the swap CP (e.g. insurer) in exchange for periodic floating payments based on the pension plan’s actual mortalities
Define cat bond
Insurance-linked debt instrument designed to transfer cat risks from issuers to investors
Why are agency relationships more important in managing private real estate than public?
- Inefficient market = cannot be certain they will receive added value
- Private access requires greater diligence
- Alpha
What is the premium of a 9 month at the money option compared to 12 months?
Value of ATM option is proportional to the square root of maturity time T, thus square root of 0.75 = 86.6%
Determine the conditions under which sale of policy is beneficial to both policy holder and entity that purchases the policy
Surrender value < Purchase price < NPV of non-surrender cash flows
Implied vs Realised Volatility
Implied: inferred under risk-neutrality, assumes:
1. Constant variance
2. Normally distributed
3. Uncorrelated
Realised: SD
1. Discrete, not continuous like Brownian motion
2. IV - Expected Realised = Vol related risk premiums
3. Same realised vol can give you different returns
