Option Returns and Individual Stock Volatility

1. 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 ynlin@dragon.nchu.edu.tw Phone: (+)886 4 22857043

2. Major Contributions & Major Findings • Interesting paper & important empirical findings. • Denote “Volatility Risk Premium” as “VRP” here. • Theoretic relation between VRP and delta-hedged 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= the volatility of the underlying stock

3. 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|highσS)– (RSelling covered calls|lowσS) ≡ 2% (on average) • Return Spreadpair trade is higher when it is more difficult to arbitrage between stock and option.

4. 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) + 

5. 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 σSare overpriced. • The existence of option momentum.

6. 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 delta-neutral 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 jumps?

7. 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?

8. 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

9. 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…

10. The End. Thank you.