Robust Option through Binomial Tree Method

Robust Option through Binomial Tree Method

Payam Hanafizadeh (Department of Industrial Management, Faculty of Management and Accountancy, Allameh Tabataba'i University, Tehran, Iran), Amir Hossein Mortazavi Qahi (Department of Financial Engineering, University of Science and Culture, Tehran, Iran) and Kumaraswamy Ponnambalam (Department of Systems Design Engineering, University of Waterloo, Ontario, Canada)
Copyright: © 2015 |Pages: 12
DOI: 10.4018/IJSDS.2015100103
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This study proposes a robust approach for pricing a European option using the binomial tree method. This method considers stock up and down prices in a closed and convex region, called the uncertainty region, defined by the covariance matrix of high and low stock prices. The option model uses this uncertainty region for pricing instead of spot prices. The method proposes an interval of prices for an option considering incidences of the worst and the best states of the stock price. The interval is flexible as it takes into account the covariance of the historical data of a stock's high and low prices and the radius of an uncertainty region.
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2. Literature Review

In this section, the option pricing models and the importance of flexibility in such models are discussed. Many researchers like Sprenkle (1961), Ayers (1963), Boness (1964), Samuelson (1965), Baumol, Malkeil and Quandt (1966) and Chen (1971) have worked on warrant pricing, but their formulae were incomplete. Since they all incorporated one or more arbitrary parameters (Black & Scholes, 1973), Black and Scholes (1973) proposed the first model for pricing a European option. There is one basic assumption in their studies: the stock price follows a random walk, and the stock price distribution at the end of each finite interval is log-normal (Black & Scholes, 1973).

Black-Scholes model's inability in pricing American options, its inflexibility against future price fluctuations, and offering a spot price as the option price are among its limitations and drawbacks.

Cox et al. (1979) proposed the binomial tree model which is a simple model in discrete time for pricing an option. They also indicated at the end of their study that by increasing the steps, the binomial tree model gets close to Black-Scholes (BS) model. Due to its discrete time structure, a binomial tree is applicable to American options (Cox, Ross, & Rubinstien, 1979). The model's complexity due to the existence of many steps and offering a spot price for the option are some of its limitations and weaknesses.

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