Are Options Mispriced Greg Orosi

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Are Options Mispriced?Greg Orosi
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Outline

• Option Calibration two methods
• Consistency Problem
• Two Empirical Observations
• Results

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Option Calibration

• Calibrating a model estimating the parameters of
  a given
• theoretical model
• There are two distinct approaches
  cross-sectional based and
• time-series based
• Cross-sectional minimize deviation between
  observed market
• prices and theoretical prices
• Time-series determine parameters from historical
  asset price

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Time Series Black-Scholes
Example volatility parameter in Black Scholes
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Cross Sectional Black Scholes

• Example Calibrating the (volatility of the)
  Black-Scholes model
• Let CT1,K1, ..., CTN,KN be market prices of
  European calls on a stock with maturities and
  strikes of (Ti, Ki)
• Let C(0,sK,T,?) be the Black-Scholes price of a
  European call with strike K, maturity T if the
  volatility equals ?
• ? Determine that value ? solving

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Crude Oil
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Advantages and Disadvantages

• Cross-sectional is forward looking contains
  more information than time series
• Time-series is not forward looking but less
  likely to misprice options

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Implied Parameters

• Consider more complex model than B-S
• We can find implied parameters for other models
  by cross-sectional calibration, and parameters
  from time-series
• Compare the two sets of parameters

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Heston model

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Implied and Actual Volatility Monthly Jan
1992-Jan 2004
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Skewness and Kurtosis
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Skewness asymmetry
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Kurtosis
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Consistency Problem

• Parameters obtained from cross-sectional
  calibration and time-series calibration are
  different
• Cross sectional values imply higher skewness
• Also imply higher kurtosis
• It seems option markets imply significantly
  different dynamics for asset than historical
  parameters consistency problem
• Which is right? Are options mispriced?
• If options are mispriced there should be
  profitable trading strategies

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Can options be mispriced?

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Yes! Before 1987 crash plot of implied
volatilities used to be flat! gt Profit by buying
OTM puts
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Option Markets

• Since 1987 crash, s tends to be low strike price,
  known as options smirk
• So option markets learned and incorporated a
  higher likelihood of a sudden large movement than
  a model based on GBM

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Empirical Observation 1

• Cause of skewness puts are more expensive than
  calls, because they can serve as insurance
  against a crash

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Shorting Puts

• Maybe there is excess return by shorting puts
• Situation reversed from before 1987 crash
• Only for stocks
• For commodities we can consider kurtosis trade
• Results later

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Possible Cause of Kurtosis

• Option market participants prefer far out of the
  money options because of large payoffs
• Causes high demand
• Willing to pay large transaction cost

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Empirical Observation 2

• Implied volatilities are higher than historical

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Empirical Observation 2

• Called negative implied volatility premium
• Implied volatilities should be higher than
  historical
• There are various risks in writing an option even
  if a market maker is vega and delta hedged
• Jump risk

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Shorting Straddles

• If the premium is high for writing an option,
  then shorting at the money straddles could
  return excess profit

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Results

• An Empirical Portfolio Perspective on Option
  Pricing Anomalies - 2005
• by Joost Driessen, Pascal Maenhout
• Analyzed options from 1987-2001 for SP500
• Accounted for jump risk and transaction costs
• Assumed power utility

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Results

• Montly CEW for different values of RA
• Under transaction cost strategies return
• 10.2 annually for short straddle (RA2)
• 18.2 (RA1)
• 11.5 annually for short put (RA1)
• 19.4 (RA2)
• Weights are negative in the portfolio for all
  values of RA

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Conclusion

• So based on data stock options ARE mispriced!
• We can use stochastic volatility parameters to
  identify mispriced options
• It is best to use a mixture of the
  cross-sectional and time-series for SV parameter
  estimation

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Thank You!

• Questions and comments!