12711

11635

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1396

دوازده، [83]ص.: مصور، نمودار

ص.ع. به فارسي و انگليسي

محمدتقي جهانديده، امير نادري

فارسي به انگليسي; انگليسي به فارسي

فريد بهرامي، محمود منجگاني

1396/05/30

كتابنامه

علوم رياضي

رياضي

ID11635

Closed Formula for Option with Discrete Dividents and its Derivatives Fatemeh shahzamani f shahzamani@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mohammad Taghi Jahandideh jahandid@cc iut ac ir Supervisor Dr Amir Naderi anaderi@cc iut ac ir 2017 MSC 97M30 97M10 Keywords Equity option discrete dividend hedging analytic formula closed formula AbstractWe present a closed pricing formula for European options under the Black Scholes model as well asformulas for its partial derivatives The formulas are developed making use of Taylor series expansionsand a proposition that relates expectations of partial derivatives with partial derivatives themselves The closed formulas are attained assuming the dividends are paid in any state of the world Theresults are readily extensible to time dependent volatility models For completeness we reproduce thenumerical results in Vellekoop and Nieuwenhuis covering calls and puts together with results on theirpartial derivatives The closed formulas presented here allow a fast calculation of prices or impliedvolatilities when compared with other valuation procedures that rely on numerical methods However the method has some signi cant drawbacks First and foremost no proof has ever beenpresent that this method would yield the correct result under an acceptable model in the sense above In fact for the natural extensions to the Black Scholes BS model described in Section 1 2 theerror grows larger as the dividend date is farther away from the valuation date This is exactly theopposite behaviour of what one would expect from an approximation a larger period of time betweenthe valuation date and the dividend date implies that the option valuation functions are smootherand thus easier to approximate The other side of the inaccurate pricing coin is the fact that thismethod does not provide a hedging strategy that will guarantee the replication of the option payo at maturity To sum up no numerical procedure based on this method returns or converges to the true value of the option in any of the acceptable models we are aware of It still seems like the

محمدتقي جهانديده، امير نادري

فريد بهرامي، محمود منجگاني