Insurance Stock Options Catastrophe Risk and the Implied

Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface Early stage paper Semir Ben Ammar University of St. Gallen, Switzerland APRIA conference Moscow, July 29 th 2014

2 Agenda 1. Motivation 2. Theory 3. Literature 4. Data 5. Empirical results 6. Preliminary conclusion and To Do Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference

3 Motivation • Property-Casualty (P&C) insurance firms are exposed to potentially large losses through catastrophic events • If extreme losses are theoretically more likely for insurance companies, this likelihood should be reflected in the implied volatility of insurance stock options • Central question: Implied volatility smile of insurance stock options more negatively sloped than non-insurance options because of anticipated catastrophe risk? Is catastrophe risk correctly priced Trading strategies due to mispricing (see 1987)? Link to ILS-market? Further explanation for what is driving the implied volatility smile! Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference

4 Theory (1/2) • P Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference

5 Literature • Two strands of literature: [1. ] Insurance stock volatility Thomann (2013): - Natural catastrophes increase the volatility of insurance stocks. - They tend to reduce the correlation of insurance stocks with the market. - 9/11 was structural break changing insurance stock betas [2. ] Implied volatility smile (IVS) - The IVS depends on net buying pressure - Leverage might also influence it - IVS seems to proxy jump risk and has negative relation with future stock prices Still some controversy what the slope measures and how it is influenced Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference

APRIA conference Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface 3 2 -1 an -J 31 0 1 -1 an -J 31 9 -1 an -J 31 8 7 -0 an -J 31 6 -0 an -J 31 5 -0 an -J 31 4 -0 an -J 31 3 -0 an -J 31 2 -0 an -J 31 1 -0 an -J 31 0 -0 an -J 31 9 -0 an -J 31 8 -9 an -J 31 7 -9 an -J 31 6 Data 60 50 40 30 20 10 0

7 Empirical results (1/8): ATM and OTM put options over time • Level of implied volatility in ATM and OTM put options of insurers and nonfinancial firms with identical realized volatility ATM options Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference OTM options

8 Empircial results (2/8): Slope of IV put options • Slope of the implied volatility function of insurers and non-financial firms with identical realized volatility Structural change through Hurricane Katherina? Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference

Empirical results (3/8): IV smiles of insurers and non-financials • Implied volatility smiles (property-casualty insurers vs. non-financial firms) 0. 44 Catastrophe risk (? ) 0. 42 Implied volatility 9 0. 4 0. 38 Mean P&C Mean non-financial 0. 36 0. 34 0. 32 -0. 25 -0. 35 -0. 45 -0. 55 Put option delta Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference -0. 65 -0. 75 -0. 8

10 Empirical results (4/8): IV smiles of insurers and non-financials • Univariate comparison of OTM put options confirm significantly different implied volatilities between insurance stocks and non-financial stocks Puts -0. 20 Mean 0. 408 P&C Mean 0. 399 nonfinancial Diff. -0. 25 -0. 30 -0. 35 -0. 40 -0. 45 -0. 50 -0. 55 -0. 60 -0. 65 -0. 70 -0. 75 -0. 80 0. 385 0. 370 0. 358 0. 350 0. 343 0. 338 0. 335 0. 333 0. 336 0. 342 0. 351 Diff. 0. 379 0. 366 0. 356 0. 349 0. 344 0. 340 0. 337 0. 009*** 0. 006* (2. 76) (1. 90) 0. 004 (1. 20) 0. 002 (0. 63) 0. 000 (0. 07) -0. 001 (-0. 23) -0. 001 (-0. 41) -0. 002 (-0. 74) -0. 004 (-1. 37) Hist. volatility 0. 326 Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference 0. 338 0. 342 0. 350 0. 361 -0. 005* -0. 007** -0. 008*** -0. 010*** 0. 019*** (-1. 83) (-2. 20) (-2. 66) (-3. 16) (6. 72)

11 Empirical results (5/8): Difference between insurers and nonfinancials • Univariate comparison of the slope of the implied volatilies smiles (property-casualty insurers vs. non-financial firms) Property-casualty insurers Non-financial firms 0. 408 0. 399 Unpaired twosided t-test N 0. 338 0. 340 0. 069 0. 059 0. 010*** (6. 86) 6636 6630 Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference

Empirical results (6/8): Event study of insurer IV 12 Event time Day -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 + - Slope of the IV-smile Coeff. 0. 019 -0. 007 0. 001 -0. 000 0. 013 -0. 010 0. 023 0. 003 0. 017 0. 012 0. 007 0. 024 -0. 011 0. 018 -0. 012 0. 003 -0. 016 0. 005 t-stat 1. 76* -0. 79 0. 16 -0. 03 1. 15 -1. 35 1. 53 -1. 28 1. 85* 0. 33 1. 74* 1. 46 0. 63 1. 33 -1. 67* 1. 59 -1. 20 -1. 44 0. 38 -1. 51 0. 43 Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference Coeff. 0. 051 0. 019 0. 008 0. 035 0. 004 0. 021 0. 022 0. 043 0. 038 0. 048 0. 026 0. 035 0. 050 0. 006 0. 025 0. 033 0. 001 0. 022 0. 031 0. 036 t-stat 4. 77*** 1. 92* 0. 85 2. 59*** 0. 36 0. 65 2. 48** 2. 09** 3. 54*** 3. 33*** 3. 70*** 2. 61*** 3. 00*** 2. 33** 0. 72 2. 13** 2. 99*** 0. 09 1. 57 2. 75*** 3. 25*** Coeff. 0. 032 0. 025 0. 007 0. 035 -0. 009 0. 014 0. 009 0. 032 0. 020 0. 034 0. 031 0. 014 0. 028 0. 026 0. 016 0. 007 0. 045 0. 013 0. 018 0. 047 0. 030 t-stat 3. 85*** 2. 69*** 0. 83 2. 88*** -1. 75* 1. 87* 1. 18 2. 87*** 2. 29** 4. 07*** 2. 70*** 1. 61 2. 91*** 1. 64 1. 96** 0. 78 3. 89*** 1. 82* 1. 68* 4. 07*** 2. 62**

Empirical results (7/8): Seasonality • Higher slope in all months Not a seasonality effect 0. 09 Slope of the implied volatility smile 0. 08 0. 07 0. 06 0. 05 0. 04 Mean P&C 0. 03 Mean non-financial 0. 02 0. 01 Month Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference ec D ov N ct O p Se g Au l Ju n Ju ay M r Ap ar M b Fe n 0 Ja 13

Empirical results (8/8): Seasonality 14 • • North Atlantic hurricane season: June 1 st - November 30 th Eastern Pacific hurricane season: May 15 th - November 30 th Mean P&C Slope of the implied volatility function Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 0. 065 0. 072 0. 067 0. 066 0. 070 0. 063 0. 078 0. 080 0. 076 0. 066 Mean non 0. 054 -financial 0. 058 0. 057 0. 059 0. 056 0. 059 0. 062 0. 063 0. 065 0. 058 0. 014*** 0. 008* Difference 0. 011*** (2. 62) (2. 97) (1. 77) 0. 010* (1. 69) 0. 007 0. 015*** 0. 004 (1. 02) (2. 89) (0. 84) Property-casualty insurers N Hurricane season (May to November) Non-Hurricane season (December to April) Unpaired two-sided ttest 0. 071 0. 067 0. 004 (1. 22) 3875 2761 Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference 0. 004 0. 016*** 0. 017*** 0. 011** 0. 008* (0. 81) (2. 89) (3. 30) (2. 02) (1. 88)

15 Preliminary conclusion and To Do • Slope of implied volatility is indeed steeper for P&C insurance stocks • Still unclear whether this steepness is the result of catastrophe risk or of another source Multivariate regression analysis is necessary • Is a trading strategy exploiting the steepness of insurance stock options profitable? TBA Insurance Stock Options, Catastrophe Risk, and the Implied Volatility Surface APRIA conference