Advanced Equity Options: Trading and Risk Management

Day One

Lessons from BSM

• Reading it as Black
  - Simpler formulas, lessons for hedging instruments
• Reading it as a book maker
  - Link to prop trading
• Reading it as Einstein 1905
  - Link expectation pricing to random walk
• The cost of dynamic hedging
• Theta / gamma ratio: the meaning
• Multiple meanings of “volatility trading”
• Estimating P&L Rules of thumb
• Thoughts on Greeks
  - Which Theta? (Part 1)
  - The general behaviour of Greeks
  - Higher order greeks: Vanna, Volga
  - Comments on Dv01 and related

Workshop: Probability and option pricing

• Pricing options from probability
• Extracting probability from market options prices
• What’s the delta?
• Excel work

Adjusting BSM Introducing some real market effects into “normality”

• Uncertainty of P&L
• Re hedging frequency impact on P&L – rule of thumb
• Transaction costs and bid/ask – rule of thumb
• When to re hedge? Different delta hedging strategies
• Relevance for bid/ask spread, portfolio effects, market making

Workshop: P&L of dynamic delta hedging simulations

• Excel work on the previous section

Breaking BSM Introducing non normality

• Non normality: good or bad?
  - Non constant vol, Stochastic Vol
  - Non normal log returns
  - Jumps
  - Feedback loops
• Gamma feedback loops and Pin Risk
• The shape of market implied probabilities
  - Reading from the volsurface
• The realized log returns probabilities
  - Skewness and fat tails
  - Which distribution fits?
  - IID? Central Limit Theorem: the old and the new
• Thoughts and consequences of non normality
  - Implications for P&L
  - Comparing realized to implied probabilities
  - Prop trading, static hedging and delta hedging

Workshop: Non normal probability distributions and jumps

• Pricing options under non normal distribution
  - Linking skewness to volsurface skew
  - Linking kurtosis to volsurface smile
  - Approximate formulas
• Excel work

Workshop: Non constant volatility

• From non constant vol to non normal probability distribution
  - Linking spot to vol correlation to distribution skewness
  - Linking vol vol to distribution kurtosis
  - Pricing options under non constant vol
• Linking spot to vol correlation to volsurface skew
• Linking vol vol to volsurface smile
• Excel work

Workshop: P&L of dynamic delta hedging Simulations Part 2

• Non constant vol effects on PL
• Jump effects on PL? Maybe not
• Feedback loop effects on PL
• Excel work

The Volatility Surface Part 1: Accounting for non normality

• Why a volsurface? What are the alternatives?
• Summary of the reasons and drivers
• The shape factors
  - Skew, Smile, Wings, Termstructure
  - Measuring them
  - Heuristic observations and behaviour
  - Different regimes and trading ranges of the factors
• From Vega to Volsurface risk
  - Calculating skew and smile exposures
  - Reporting Vega by buckets
  - Pitfalls
  - Comparison to Volga and Vanna
  - Link to exotics
• The dynamics
  - Stickiness and other modes
  - Realized dynamics
  - Effect of different dynamics on delta
  - Three ways to trade skew
  - Other volsurface plays

Examples: Studying and aggregating risks in vanilla portfolios

Day Two

Interlude: Model independent early exercise for American options
Case study: from vanilla portfolios trading to model independence

• Reducing the hedging error when trading realized vol with vanillas
• The famous “log portfolio” vs. less famous portfolios
• Comparison to variance swaps, volatility swaps, VIX, etc.

Case study: “Black Swan” hedging

• Comparing different instruments
  - OTM puts and put spreads
  - Variance swaps plus vanillas combinations
  - “Crash puts” and daily cliquets
  - Best of puts
  - VIX options?
• Highlighting differences
• Estimating value vs. typical market prices

Day Three

Not so simple: dividends, repos and discount factors

• What’s the right discount factor?
• One or two yield curves?

Case study: “Collateral Damage” – the Warren Buffett puts

• Rule of thumb to price the correlation spot to CDS
• Dividends (what makes equity derivatives harder than forex)
  - Absolute, proportional, mixture
  - Effects on deltas
  - Effects on volsurface
  - American vs. European quasi arbs
  - Consequences for volsurface representation and interpolation
  - Impact on variance swaps
  - Impact on European / American / Exotics
  - Why everybody uses non consistent dividend models in practice
  - Avoiding rookie mistakes
  - Same strike, different vols?

Case study: Dividend Risk – Blowing up on dividends in 2008

• The spot to div feedback loop and what drives it
• The market flows that drive implied dividends, impact of exotics and variance swaps
• Hedging
• Measurements
  - Repos aka Borrow costs
  - Going Japanese? Negative repos
  - Markets flows
  - Impact on long term derivatives and structured products
  - Is there an arb? How?
  - Delta effects
  - Consideration on structured products hedging
  - Test Skew, Smile, Wings, Termstructure
  - Measuring them
  - Heuristic observations and behaviour
  - Different regimes and trading ranges of the factors

Workshop: Calculating the “put floor” for volsurface from credit risk

What we learn from free lunches and quasi arbs

• Volsurface skew: the simplest free lunch
• Why sticky strike is arbitrageable
• Why sticky moneyness is no better
• Thoughts and consequences
  - Delta and theta are wrong
  - Using delta to hedge vega?
  - The need for stochastic vol

Quick review of volatility models from a vanilla trader point of view

• Just the essentials... why they matter
• Local Vol – e.g. Dupire, Derman Kani
• Stochastic Vol – e.g. Heston, SABR
• Stochastic Local – The future?
• Others?
• Thoughts and practical consequences

What’s my Delta? What’s my Theta?

• Why and to whom VolSurface dynamics matter
• Different approaches to correcting the delta
  - Sticky strike, sticky moneyness delta
  - “Skew delta”, “Shadow delta”, “Swimming delta”, etc.
  - LV delta, SV delta
  - “Beta” delta
  - Minimum variance delta
  - What to do with theta?
  - Examples, comments and current practices

Workshop: Calculating delta with different dynamics

The Volatility Surface Part 2

• Far OTM: the wings
  - Why they matter
  - Empirical evidence
  - Theoretical asymptotics
  - Can we learn from variance swaps prices?
• The representation dilemma
  - Parameterization, interpolation or grid of numbers?
  - Pros and cons of each one
  - Which vol? Implied or local?
• Consequences for stress reports and risk management
• The extrapolation issue
• Different tools for different needs: pros and cons
• The pitfalls of a non parametric volsurface
• The x axis: F/K? Delta? Others?
• Global vs. timeslices: pros and cons
• Review and comments on existing ones:
  - Well known parametric volsurfaces
  - SVI
  - SABR
  - Heston
  - Assorted polynomials, NIGs, etc
  - Less well known ones
  - Cost based, Carr Wu style
  - Global and/or proprietary
• Relative value vol trading: the problem of comparing volsurfaces

Building volsurfaces from scratch

• Similar problems:
  - The illiquid surfaces with just a few quotes
  - Extrapolating beyond the last liquid maturity
• What goes in the shape, what goes in the bid/ask
• Review of the approaches available
• Analysis of past data
• Derivation from liquid surfaces
• “Breakeven skews” analysis
• Other considerations
  - Basketization thoughts
  - Total Return vs. Price Return
  - The Credit Put Floor
  - Leland