Question

" The Black-Scholes and Merton method of modelling derivatives prices was first introduced in 1973, by the Nobel Prize winners Black, Scholes (1973) and Merton (1973), after which the model is named. Essentially, the Black-Scholes-Merton (BSM) approach shows how the price of an option contract can be determined by using a simple formula of the underlying asset’s price and its volatility, the exercise price – price of the underlying asset that the contract stipulates – time to maturity of the contract and the risk-free interest rate prevailed in the market". (i) Critically assess the merits and shortcomings of the Black Scholes Pricing Model on the Stock Exchange of Mauritius.

Answer 1

Merits

The Black-Scholes option pricing model allows to calculate the a very large number of option prices very quickly. The BS option pricing model is considered to be very fast as compared to any other option pricing methodology. Moreover the pricing model is very simplistic in application and assumption, allowing the users to calculate a benchmark of option prices over the exchange.

Shortcoming of the BS model

The BS model is completely theoritical in nature and does not accurately describes the option prices on the Stock exchange. The biggest shortcomings is related to its assumptions and calculation of volatility. The model does not distinguish between explicit and implicit volatility Here, the implicit volatility is the one that satisfies BS model. These implicit volatility itself takes many forms such as skews, volatility smiles. Also, if we observe the  Stock Exchange of Mauritius, often option contracts are traded in blocks, whereas in the BS model it asset indivisibility is an assumption. Also, the model assumes a random walk ie geometric brownian motion pattern, whereas on the stock exchange it is observed that many large price swings are observed.