A Modal Approach To Price An Option In Continuous Time
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Date
2018
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Publisher
KNUST
Abstract
Average value options or Asian options have been priced using geometric and arithmetic averages of the underlying asset. However, these methods do not give accurate results especially in very low volatility regimes. In this study, we develop a new option pricing model based on the modal average of the underlying asset to price options. Using data from the NASDAQ in the United States of America we use the proposed model to price options sold on some stocks listed on the exchanges using software. The results consistently showed that for volatilities less than 3% of the underlying asset, the modal average option pricing model gives a better option price when compared to existing average option pricing models. Moreover, the modal average consistently does better at all levels of volatility when compared to the Black-Scholes model. We further proved analytically that the modal average model indeed does better than the geometric or arithmetic average models especially for low volatility stocks.
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THIS THESIS IS SUBMITTED TO THE DEPARTMENT OF MATHEMATICS, KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF DOCTOR OF PHILOSOPHY (PhD) IN APPLIED MATHEMATICS