تسعير الخيارات الامريكية على مستقبليات مؤشرات الاسهم باستخدام نموذج بارون ووايلي التقريبي

Pricing American Option on The Futures of Stocks indexes By Using Barone and Whaley's Approximate Model

Abstract :

Financial markets suffer from the changes in the pricing levels , and this is called pricing risk . Stock indexes are but immediate financial tools that are directly affected by such a risk . Accordingly , new financial tools are invented such as financial derivatives using these tools, especially futures options requires a model for pricing them , particularly if it is made known that these options have two exercise styles : European and American. European options pricing models are available in the form of Black̓s model and binomial model. The problem of the study lies in pricing the American option , which is represented by testing an approximate analytic model for pricing American options on the futures of stock indexes . It also lies in knowing whether Barone and whiley’s approximate analytic model is precise in piecing American futures options in comparison with European options pricing model. this firstly requires testing the preciseness of the pricing model for the contracts of the futures of the underlying index ( the classic holding cost model versus the adjusted model for the dividend yield ) is standing at the most Precise model as a preliminary for testing the preciseness of the pricing model for European futures options (Black and binomial) , and comparing them to see the most precise between them . then the , latter is compared to Barone and whiley’s model for American futures options , after analyzing its preciseness . the study is based on the daily close prices for the index(S&P500), which is the underlying index for New York stock Exchange (NYSE) , and for the daily settlement prices for the futures contract of the index (S&P500) in September 2012 from the first trading day available till the maturity day of the contract from Chicago Merchant Exchange (CME) where the contract is trading . the two European calls and puts on index futures are priced by using binomial and Black’s models for different periods . On the other hand , the tow American calls and puts on index futures are priced by using Barone and Whiley’s model . through using various statistical , financial and mathematical models the study reaches at a number of conclusions , the most important of which are : 1- Black’s model proved its preciseness in pricing European options on the stock indexes futures . this supports the practical results of pricing futures option of stock indexes. 2- The Practical results proved that the more the number of periods for the binomial model , the more it is close from the preciseness of blacks model for pricing European options on the stock indexes futures 3- The approximate analytic Baron and Whiley’s model is much more precise in pricing American Futures Options for its success in incarnating the early exercise value for the American option , which could not be reflected in the premium of the option by Blacks model. In the light of the above , the study recommends the following : 1- In the light of the great market price risk that dealers face in Iraqi stock market , it becomes necessary to establish market for financial derivatives in general , and for stocks and stock index derivatives in specific in other to hedge this risk . 2- To ensure the pricing efficiency for the suggested market , dealers have to depend on the most precise pricing model whether for underlying asset or for derivative contract ( simple or complex) .