A.M. Kimiagari & E. Afarideh Sani

Transcript

1 - UGGETION A COMPOED OPTION PRICING MODEL BAED ON BLACK-CHOLE AND BINOMIAL TREE MODEL (CAE TUDY IN TEHRAN TOCK EXCHANGE) A.M. Kimiagari & E. Aarieh ani Department o Inustrial Eng, kimiagar@aut.ac.ir, ehsan.aarieh@gmail.com Abstract: This paper suggests a compose option pricing moel base on black-scholes an binomial tree moels. o at irst this two moels are presente an analyze. Then we showe black-scholes moel is an appropriate option pricing moel or stocks with low an binomial trees moel is an appropriate option pricing moel or stocks with high. uggeste moel is a compose moel o black-scholes an binomial tree moels an is use as selecting moel actor. To etermine limit quantity, we calculate average o Iran tock Exchange. For this calculating we selecte 3 stocks in two perio o time. At the en o paper, suggeste moel is valiate by methos an it s valiity is approve by both o them. ( ) : :..... // : // : kimiagar@aut.ac.ir ehsan.aarieh@gmail.com

2 P : δ : u = e = e = e = e rδt [ Puu + (1 P) u ] rδt [ Pu + (1 P) ] rδt rδt [ Pu + (1 p) ] [ P : () () uu + P(1 P) u + (1 P) u ] () () () () : u u = e δ Δt rδt e P = u. = e ( ) δ Δt (1 P ) P(-P) P () ().. u. (back ) war) (.[].-...[-] : : t: s: (T).[].. u>1) u r.( <1. Δt u u. :[-] x x :

3 .. Put-Call Parity : ( ) ( ) ()..- ( t) P Xe = N N 1..[]. ( ).[]..[]..[].[]. at the money in the money. money out o the.[] 1 T φ : N: : r: 1 + rs + δ t = r..-- max( X,0) T :[] () ( t C e = ) [max( X ),0] T ln T δ ln T ~ φ ln + r ( T t), δ T t : () : () () C = N ( ) Xe N ( ) 1 ln = X ( t) 1 δ + r + δ T t ( T t ) δ ln + r ( T t) X + = = 1 δ T t δ T t : () : () (). ( t) ( t) C = e N( 1) e XN( ) ()

4 :. /. : : : : : : : : : : /..[].[].-... ).[] (.[]..[]....

5 ... : : :

6 +,. -, +, -, : :.. ( ).. : :. % % [- ].....

7 :. = Pe :[] () :[] I ( T -X)<0 I ( T -X) < 0 Pe X T Pe () [] : = X Pe t () C, P X:. : = Pe. [] () :[] i ( T X) > 0 T X Pe i ( T X) < 0 Pe ( ), // :,, // //, //., //, // :[],, // // = X T Pe ().

8 : question1 question question3 question4 question5 question6 Item tatistics Mean t. Deviation N µ 3. <µ. - : : +, -, +, -,. : +,. -, ,. -,

9 .. [1] Hsia, C., On the Binomial Option Pricing. The journal o inancial research, 1983, PP [] Oluemi olusola, Oegbile. "Binomial option pricing moel". Arican Institute or Mathematical cience, Ross, helon. An elementary introuction to mathematical inance: options an other topics. th e. America: Cambrige university press, 003. [3] Black, F.; choles, M., The Pricing o Options an Corporate Liabilities, Journal o political economy, vol 86, 1973, P.637. [4] Clarkson, Robert; Bank, Cherry. "ome Observations on the Black-choles Option Pricing Formula", Dubosky, Davi A. options an inancial utures: valuation an use. 1th e. America: Mc Graw-Hill, 199. [5] Garven, James. "Derivation an Comparative tatic s o the Black-choles Call an Put Option Pricing Formula". athematical science, New York university, anuary 15, 00. [6] Greenspan, A., "Financial Derivatives". Remarks by chairman o eeral reserve bank to Futures inustry association, Floria, march 19, [7] Hull, juhn, C., Options, Futures, an Other Derivatives. 3th e. Toronto: University o Toronto, [8] Irwin, Richar D., Option Volatility an Pricing, Avance Traing trategies an Techniques. 1th e. America: Mc Graw-Hill companies, [9] McMillan, L. Options as a trategic Investment. 4 th e. New York:New York institute o inance, 00. [10] Roman, teven. Introuction to the Mathematics o Finance: rom Risk Management to Options Pricing. 1th e. America: springer, 004. [11] Rubinstein, M. Derivatives Assets Analysis. The journal o economics perspectives, 1987, PP ".. [].."." P13 ". [].. [].. : - : : : : : : : :.. : :. :. : :. :. : %. spss question1 question question3 question4 question5. Binomial Test > Observe Exact ig. Category N Prop. Test Prop. (1-taile) Group 1 <= a Group > 3 Group 1 <= a Group > Group 1 <= a Group > Group 1 <= a Group > Group 1 <= a Group > Group 1 <= a question6 Group a. Alternative hypothesis states that the proportion o cases in the irst grou