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Option Returns and
Individual Stock Volatility
10 December 2010
Jie Cao, Bing Han
Chinese University of Hong Kong, University of Texas at Austin
Discussant: Yueh-Neng Lin
National Chung Hsing University
[email protected]
Phone: (+)886 4 22857043
1
Major Contributions
& Major Findings
• Interesting paper & important empirical findings.
• Denote “Volatility Risk Premium” as “VRP” here.
• Theoretic relation between VRP and deltahedged option returns: Bakshi and Kapadia
(2003a).
• This paper points out the existence of VRP in
individual stock options by empirically finding
• for most stock options, delta-hedged option return=
delta-hedged option gain(t,t+τ) /St <0
• |delta-hedged option gain(t,t+τ) /St|= f(σS(+) , …) , where σS =
2
the volatility of the underlying stock
Major Contributions
& Major Findings (continued..)
• delta-hedged option gain(t,t+τ)= f(systematic volatility risk
σmsystematic , aggregate idiosyncratic volatility risk
σmidiosyncratic , option market makers’ unhedged
position risk, option market inefficiency, …)
• Strategy conditional on σS:
• Return Spreadpair trade= (RSelling covered calls|high σS)– (RSelling
covered calls|low
σS) ≡ 2% (on average)
• Return Spreadpair trade is higher when it is more difficult
to arbitrage between stock and option.
3
Major Contributions
& Major Findings (continued..)
• Delta-hedged option return = *+
1Rm+2SML+3BM +4momentum+5σmsystematic
+6σmidiosyncratic
+7stock_liquidity(=Amihud illiquidity measure)
+8pice_jump
+9option_oi(=option demand)
+10option_vn(=option liquidity)
+11volatility-related mispricing(=realized
volatility-implied volatility) + 
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Major Contributions
& Major Findings (continued..)
• |VRP|= g(σS(+), extraRPoption sellers(+), …)
• extraRPoption sellers = compensation for option sellers
who are unable to eliminate individual stock
volatility risk.
• Option prices with high σS are overpriced.
• The existence of option momentum.
5
Questions & Suggestions
• On page 6, what is the meaning of “We control for
any remaining difference in option moneyness
using option’s vega”?
• What kind of volatility used to calculate daily
delta when constructing daily rebalanced deltaneutral option portfolio?
• This paper also estimates VRP by controlling for
exposure to price jump risk. Given the possibility
that price jumps are usually accompanied with
volatility jumps, do the results in this paper
underestimate |VRP| contributed by volatility
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jumps?
Questions & Suggestions
(continued..)
• On page 23: “…under limits to arbitrage, option
prices are affected by the demand pressure.”
• It is interesting to further investigate elaborate
possible reasons responsible for the limited arbitrage
situations here.
• Also, it could be possible to link the arbitrage
limitation reasons with option demand pressure.
• When market makers face the hedger’s demand
pressure, to what extent the extra costs is asked
by the market makers?
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Questions & Suggestions
(continued..)
• Possible reasons to explain the option
momentum could include
• Volatility persistence
• Volatility clustering
• Characteristics of volatility term structure
• Possible economic source of strong negative
individual volatility risk premium could be
• Market makers’ extra compensation
• The “real” negative volatility risk premium
• Investors’ fears
• Market makers’ hedging costs
• Other option market liquidity measure
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Questions & Suggestions
(continued..)
• Other than options’ bid-ask spreads as option
costs, how about the upfront option payments
and implicit cost over the holding periods?
• More illustrations on the impact of discrete
trading, big jumps, volatility jumps, stochastic
volatility on options costs…
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The End.
Thank you.
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