Date post: | 25-Dec-2015 |
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State of the MarketsWhat’s been going on?
• U.S. homebuilders- confidence drops– Seasonal or something
else?
• Greece – No to bailout extension– Closer to euro exit?
• Oil– BP’s report
Equities
• What do you own?
• How do you make money?
• Preferred vs. Common Stock
• Equity Fundamentals Equity
Preferred Equity
Mezzanine
Unsecured Bonds
Secured Bonds
Bank Debt
Options
• What does it mean to have an option?• Who has the obligation to perform a duty,
who has the option to take action?• What is a derivative?
Options
• Right to buy (or sell) something at a certain point in time
• But you don’t have to if you don’t want to
• Drivers?– Underlying/Spot– Strike– Dividends– Interest Rates– Time– Volatility
Difference between Stocks and Options
• Regular equities can be held indefinitely… options have expiration dates– If an OTM option is not exercised on or before
expiration, it no longer exists and expires worthless
• No Physical certificates for stock options• No ownership – owning options doesn’t confer
voting rights, dividends, ownership, etc.– Unless option is exercised
• Fixed number of stocks issued by company• Opportunity for Leverage
Naked Options
• A “naked” option position is a portfolio consisting only of options of a given type (i.e. calls or puts)
• 4 kinds of naked options positions– Long Call– Short Call– Long Put– Short Put
Purpose
• Options offer one-sided protection against price moves– Instruments of *financial insurance*– Call: provides protection against an increase
in price– Put: provides protection against a decrease in
price
• Can be used to take positions on market direction and market volatility– Bullish on vol: long options,– Bearish on vol: short options
Risk Management
Options Strategies
• Presence of non-linearity in their payoffs– Options can be combined into portfolios to
produce precise and targeted payoff patterns
• Two components of an option premium: – Intrinsic Value: ITM portion of the option
premium• Alternatively, value that any given option would have
if expired today
– Time Value = Option Premium – Intrinsic Value
Factors Affecting Option Prices Strike Price Stock Price Implied Volatility Time to expiry Risk-free rate
Exotics
• Any option different from vanilla options• Not necessarily more complex– Digital options have simple structures– Can be complex – barriers, Asians, quantos
• Why use exotics?– Richer payoff patterns/costs
• Insurance contracts with greater flexibility
Put-Call Parity
The equation follows as such: c + PV(x) = p + s
This relationship tells us that going a long a call (+C) and shorting a put (–P) will yield a function that resembles a Forward
C - P = F
Put-Call Parity
The equation follows as such: c + PV(x) = p + s
This relationship tells us that going a long a call (+C) and shorting a put (–P) will yield a function that resembles a Forward
C - P = F
Some interesting exercise tactics When do you exercise an American
call early? When do you exercise an American
put early?
The Greeks: Delta
Mathematical Definition dV/dS
What does it mean? The change in the option’s value per $1 change in
stock price How do we think about it intuitively?
Probability of the option finishing in the money Important Graphs
Delta v. Spot (at different times) Delta v. Time to Expiry (with different moneyness)
The Greeks: Gamma
Mathematical Definition dΔ/dS = d2V/dS2
What is it? The change in the option’s delta per $1 change
in stock price How do we think about it intuitively?
How convex is your option price? How fast does your option value accelerate?
Graphs Gamma vs. Spot (at different times)
The Greeks: Theta
Mathematical Definition dV/d(T-t)
What is it? The change in the option’s value for 1 day
passing How do we think about it?
How much am I paying to hold this option for a day?
Graph Theta decay
The Greeks: Vega
Mathematical Definition dV/dσ
What is it? The change in the option’s value per 1%
change in implied volatility How do we think about it?
What is the size of my volatility position? Graphs
Vega vs. Spot (at different levels of IV)
The Greeks: Vanna
Mathematical Definition dVega/dS = dΔ/dσ = d2V/dSdσ
What is it? The change in the option’s Vega per $1
change in spot How do we think about it?
What is the size of my skew position?
The Greeks: Volga
Mathematical Definition dVega/dσ = d2V/dσ2
What is it? The change in the option’s Vega per 1%
change in implied volatility How do we think about it?
How much does my option benefit from vol on vol?
Volatility Skew
Definition The difference between OTM and ATM IV
How do we think about it? How much does my IV change with a change
in spot? Three main positions
ATM Straddle 25-delta Risk-Reversal 25-delta Butterfly
Volatility Skew (Continued)
How to compare IV across term structures and skews? Use square root of time rule to normalize
You can use this to make relative value vol trades Can stay vega-neutral and just take advantage
of the pricing discrepancy
Gamma Scalping
You think implied volatility is very low relative to historical/realized volatility. How do you take advantage of this situation?
Calendar Spreads Trading
If a surface rises with power < .5: Short calendar
If a surface falls with power < .5: Long calendar
If a surface rises with power > .5: Long calendar
If a surface falls with power > .5: Short calendar
Trading Situation
You are looking at the term structure and skew of implied volatility. You notice that options with longer maturities have higher IVs than shorter dated options. You also notice that there is some pretty strong skew (OTM put IVs are much higher than ATM put IVs).
You think that realized vol will pick up soon, while long-term vol will be lower than the OTM puts suggest. What do you do?