PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

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730 APPLICATION OF THE OPTION MARKET PARADIGMREFERENCES[1] Mildenhall, Stephen J., Discussion of “Application of theOption Market Paradigm to the Solution of Insurance Problems,”PCAS LXXXVII, 2000, pp. 162—187.[2] Wacek, Michael G., “Application of the Option MarketParadigm to the Solution of Insurance Problems,” PCASLXXXIV, 1997, pp. 701—733.[3] Moller, Thomas, “Risk-Minimizing Hedging Strategies forUnit-Linked Life Insurance Contracts,” ASTIN Bulletin, 28:1,1998, pp. 17—48.[4] Moller, Thomas, “Stochastic Orders in Dynamic ReinsuranceMarkets,” http://www.astin2003.de/img/papers/moeller.pdf,presented at 2003 ASTIN Colloquium and to be publishedin Finance and Stochastics.[5] Esipov, Sergei, and Dajiang Guo, “Portfolio Based Pricingof Residual Basis Risk with Application to the S&P 500 PutOptions,” CAS Discussion Paper Program, May 2000, pp.43—66.
APPLICATION OF THE OPTION MARKET PARADIGM 731APPENDIX AMEAN AND VARIANCE OF A SIMPLE BUY-AND-HOLD OPTIONHEDGELet h = bx ¡ y define a random variable for the value at expiry ofa hedged portfolio comprising b shares and one short call (i.e.,sold short). Here x is a lognormal random variable representingthe stock price distribution at option expiry, and y is the randomvariable representing the value at expiry of the call option on thestock. The option strike price is denoted S.Mean of Hedged Portfolio at ExpiryE(h)=E(bx ¡ y)= bE(x) ¡ E(y)= bE(x) ¡ (E(x) ¢ N(d (¹)1 ) ¡ S ¢ N(d(¹) 2 ))=E(x) ¢ (b ¡ N(d (¹)1For the special case of b = N(d (¹)1 ),)) + S ¢ N(d(¹)2): (A.1)E(h)=S ¢ N(d (¹)2): (A.1a)Second Moment of Hedged Portfolio at ExpiryE(h 2 )=E((bx ¡ y) 2 )=E(b 2 x 2 ¡ 2bxy + y 2 )= b 2 E(x 2 ) ¡ 2bE(xy)+E(y 2 )= b 2 E(x 2 ) ¡ 2b(E(x 2 ) ¢ N(d (¹)0) ¡ SE(x) ¢ N(d(¹)1 ))+(E(x 2 ) ¢ N(d (¹)0) ¡ 2 ¢ SE(x) ¢ N(d(¹)1 )+S2 ¢ N(d (¹)2 )):=(b 2 + N(d (¹)0 ) ¢ (1 ¡ 2b)) ¢ E(x2 )¡ 2S ¢ N(d (¹)1 ) ¢ (1 ¡ b) ¢ E(x)+S2 ¢ N(d (¹)2): (A.2)
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VOLUME XCII NUMBERS 176 and 177PROC
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FOREWORDActuarial science originate
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2005 PROCEEDINGSCONTENTS OF VOLUME
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2005 PROCEEDINGSCONTENTS OF VOLUME
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Editorial Committee, Proceedings Ed
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2 AN EXAMINATION OF THE INFLUENCE O
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RISKINESS LEVERAGE MODELSRODNEY KRE
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DISCUSSION OF A PAPER PRESENTED AT
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RISKINESS LEVERAGE MODELS 81EXHIBIT
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WHY LARGER RISKS HAVE SMALLER INSUR
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ADDRESS TO NEW MEMBERS 151ateship a
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ADDRESS TO NEW MEMBERS 153You shoul
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ADDRESS TO NEW MEMBERS 155strength
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MINUTES OF THE 2005 CAS SPRING MEET
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MINUTES OF THE 2005 SPRING MEETING
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Volume XCII, Part 2 No. 177PROCEEDI
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WHEN CAN ACCIDENT YEARS BE REGARDED
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ARCHITECTURE FOR RESIDENTIAL PROPER
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ESTIMATING THE WORKERS COMPENSATION
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REPORT OF THE VICE PRESIDENT-ADMINI
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2005 EXAMINATIONS—SUCCESSFUL CAND
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OBITUARIESROBERT GRANT ESPIECLYDE H
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OBITUARIES 825SIDNEY M. HAMMER1931
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OBITUARIES 827J. GARY LaROSE1947—
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OBITUARIES 829PAUL J. SCHEEL SR.193
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OBITUARIES 831LEO M. STANKUSCirca 1
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INDEX TO VOLUME XCIIPage2005 EXAMIN
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835GRAVES, CLYDE H.INDEX—CONTINUE
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837INDEX—CONTINUEDREPORT OF THE V
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PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

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