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The first criterion is to see whether the valuations from the application of the model conform to reality or are close to the actual trading prices and whether the assumptions can be met.
Some studies show that the Black-Scholes model seems to perform poorly for valuing deep in the money calls and deep out of the money calls. Deep in the money calls are always undervalued and deep out of the money calls are overvalued. Other studies focus on the reality of the assumptions. Geske and Roll  have pointed out that the reason of the observed empirical mispricing by Black-Scholes model is that the model fails to consider two factors - the early exercise possibility and that the underlying stocks pay dividends.
According to the assumptions, the volatility implied by the Black-Scholes option model with different exercise prices (E) and the time to maturity (T) should remain constant over time. And the implied volatility should be consistent with the actual volatility observed in the underlying stock market. But this hypothesis is always violated in real world. Rubinstein  has argued that the implied volatility does not stay constant. It is a decreasing function of exercise prices and can be an increasing or decreasing function of the time to maturity. He also found that the volatility implied by the Black-Scholes option model is different from that observed directly from underlying stocks.

Whether there is a better model could be the second criterion. There are two basic option valuation models – binomial option pricing model and Black-Scholes option pricing model. The binomial option pricing model is simple in its formula term. It allows the underlying stock price to go either up or down, possibly at different rates which follow a binomial probability distribution. That the probabilities to go up or down are available and constant over time and that risk free rate is constant over time are assumed in the binomial model. Unlike the Black-Scholes model, it can value early exercise American options and the options with the underlying stocks which pay dividends. Although the binomial option pricing model is more flexible and simple in its formula term, it requires a computer program to run the complex algorithm involved. The binomial model is a discrete time model whereas the Black-Scholes model is a continuous time model. The results generated from the binomial model converge to that of the Black-Scholes model as the number of time intervals increases. Both models are important and widely used in practice.
There are numerous advanced models emerging in the recent financial literatures. However, most of them come from the basic structure as the Black-Scholes model. GARCH model (Generalized Autoregressive Conditional Heteroskedasticity) has gained widespread acceptance in the literature. The model relaxes the critical assumption of the Black-Scholes model – homoskedasticity, however, it become much more complex and not widely applied in practice.

The third criterion is whether the model is widely used in practice. There is no doubt that the Black-Scholes model is widely applied in practice and in the literature as well. Most market participants apply this model to value options, hedge their portfolio positions and generate implied volatilities.

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Bibliography:

Bodie, Z., Kane, A., & Marcus, A. J. (2002). Investments (5th Ed.). Boston: McGraw-本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。