Black-Scholes model is essentially a formula used in the calculation of a theoretical call price for options. It is considered to be the fundamental model for pricing in the option market (Cretien, 2006). This model uses in its calculation the five main determinants of an option's price, which include stock price, strike price, volatility, time left until expiration, as well as risk-free, short-term interest rate (Hoadley, 2010). The computations executed by the Black-Scholes model result in prices that are close to actual market value as long as input variables are determined that are reasonably accurate (Cretien, 2006). A benefit resulting from the use of this model is that it provides traders with a means to compare market prices with alternative values while using different inputs (Cretien, 2006). The Black-Scholes model also assists in the prediction of movements in price for investments other than options by providing a way to compute implied variance for any assets that have options traded (Cretien, 2006). Moreover, the Black-Scholes model may be defined as a method for the theoretical pricing of options that is based primarily on risk-free arbitrage between options on the assets' prices and underlying assets The Black-Scholes model is considered as the most fundamental formula for pricing options (Crawford, 2003). It forms the basis for all option-pricing models (Cretien, 2006). Without the Black-Scholes model, the market for exchange-traded options would not exist as it currently does (Cretien, 2006). There have been subsequent models developed for price calculation of options, but it may be understood that these are merely variations on the Black-Scholes model (Crawford, 2003). The Black-Scholes model is considered by many to be irreplaceable, although it has some limitations as to how effective it is for the valuation of various types of options (Cretien, 2006). The concept on which the Black-Scholes model...
The main characteristic of a lognormal distribution in comparison with a normal bell curve is that the lognormal distribution exhibits a longer right tail (Hoadley, 2010). This type of distribution allows for any possible stock price between zero and infinity and does not allow for any negative prices (Hoadley, 2010). Furthermore, a lognormal distribution also exhibits an upward bias, which represents how a stock price can only drop 100% of its worth but can rise by more than 100% of its worth (Hoadley, 2010). However, distributions of underlying asset prices often significantly depart from the lognormal, and the pricing executed by the Black-Scholes model can be modified in order to effectively deal with non-lognormally distributed asset prices (Hoadley, 2010).
Black-Scholes Option Pricing Model was developed in the 1970s as a way to generate a legitimate and accurate valuation model for stock prices based on specific circumstances in the market and the stock options. It is the creation of economists Myron Scholes and Fischer Black who aimed to better forecast call options at various times within the option life cycle (PBS, 2000). According to the research, "this work involved calculating
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The model assumes a normal distribution, so the greater the time to expiry, the greater the expected fluctuation in the stock's price. Thus, if the option is in the money, the greater the risk that it will expire out of the money; if the option is out of the money, the greater the likelihood that it will expire in the money. The risk-free rate is also important, because the
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