European Option Pricing Using Truncated Normal Distribution
Abstract
Option trading is one of the activities that take place in the nancial market. Pricing
these option is key for investor to ensure that the position they take o ers good returns.
The Black & Scholes model is widely used in pricing option although its underlying
assumptions are inconsistent with the market dynamics. Some studies have been done
aimed at improving the Black & Scholes model and in general the pricing of option.
In this paper, we take the same motive but now use the truncated normal distribution
instead of the normal distribution that as been used in previous studies. Under the truncated
normal distribution, denoted by TND in this paper, the underlying asset’s log-return of
is assumed to be bounded below and above. The boundary values are determined by the
investor’s perceived realistic price ranges of the underlying asset. The basic statistics of
the proposed model are derive. The martingale restriction and closed formulas for option
pricing as well as the pricing error are presented. The put - call parity and duality and some
of the Greeks are also formulated. From the numerical result of the study, the proposed
model performs better than the classical Black & Scholes at di erent price ranges for
European options.
Publisher
University of Nairobi
Rights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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