Quantitative Finance Society Options, explained

State of the Markets What’s been going on?

State of the Markets What’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

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

Advanced Options

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 = d 2 V/dS 2  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 = d 2 V/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 = d 2 V/dσ 2  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?

Questions?