Pricing American options on stock index futures using the approximate Barono-Wiley model - an applied study on data from the New York Stock Exchange and the Chicago Mercantile Exchange

Abstract

Financial markets suffer from fluctuations in price levels, which is called price risk. Stock indices are just one of the immediate financial instruments that are directly affected by this risk. This problem has led to the creation of new financial instruments such as financial derivatives. The use of these instruments, especially futures options, requires a model for pricing them, especially if we know that these options have two types of execution (European and American), and that European options pricing models are available, such as the Black model and the binomial model. The problem lies in the pricing of the American option, which is the essence of the research problem, which is represented in trying to test an approximate analytical model for pricing American options on stock index futures and knowing whether the approximate analytical model of Baron and Wiley is accurate in pricing American futures options compared to the European options pricing model. This required, first and foremost, testing the accuracy of the basic index futures contract pricing models (classical holding cost model versus modified dividend yield model) and identifying the most accurate model in preparation for testing the accuracy of the European futures options pricing models (Black and binomial) and comparing them and identifying the most accurate of them, and then comparing the most accurate of them with the Baron and Wiley model for American futures options after analyzing the accuracy of the latter. The study relied on the daily closing prices of the (S&P500) index, which is the basic index of the New York Stock Exchange (NYSE), and the daily settlement prices of the (S&P500) index futures contract in September 2012 from the first trading day that could be obtained until the contract's maturity date from the Chicago Mercantile Exchange (CME) where this contract is traded. The European options contracts for buying and selling index futures were priced using the Black and Binomial models (for different durations), and the American options contracts for buying and selling index futures were priced using the Baron and Wiley model. Using several mathematical, financial and statistical models, the study reached a number of conclusions, the most important of which are:

The Black model proved its accuracy in pricing European options on stock index futures. This supports the applied results for pricing stock index futures options. All the results extracted according to the Black model confirmed that it is accurate in pricing European options.
The applied results proved the fact that: the more the number of time periods of the binomial model increases, the closer its accuracy is to the accuracy of the Black model for pricing European options on stock index futures.
The Baron and Wiley approximate analytical model is more accurate in pricing American futures options due to its success in embodying the early execution value of the American option, which the Black model failed to reflect in the option premium.
In light of the above, the study reached a number of recommendations, the most important of which are:

In light of the large market price risk faced by traders in the Iraqi Stock Exchange, it has become imperative to establish a market for financial derivatives in general and for stock derivatives and the market stock index in particular in order to hedge this risk.
To ensure the pricing efficiency of this proposed market, traders must rely on the most accurate pricing models, whether for the underlying asset or the derivative contract (simple or complex), and this is the focus of this study.