What are the assumptions of Black Scholes Model of valuing options contracts?

The Black Scholes Method works with three different types assets −

• The risky assets
• The riskless assets, and
• The option of the risky asset whose value has to be found.

Depending on the type of assets, there are four categories of assumptions that the Black Scholes method follows, which are −

• Assumptions about the underlying risky asset
• Assumptions about the underlying riskless assets
• Assumptions about the options
• Assumptions about the market

Assumptions about risky assets

The risky assets such as stocks and bonds have the following assumptions under the Black Scholes model −

• Random walk − It states that the direction of a risky asset can be gauged but its direction cannot be pre-determined. That is a stock’s price may go up or down but we cannot definitely say upward or downward.

• Constant volatility − The Black Scholes method assumes that the volatility of the options is constant and known beforehand. In the practical world, it is neither possible to find constant volatility and nor can we find a pre-known asset price.

• Normally Distributed Returns − Due to the random price of the assets, the return on risky paths of assets is normally distributed. In other words, the future stock prices at a certain time will be lognormally distributed.

• No Dividends − There will be no dividends paid in the lifetime of an option. Dividends are paid for stocks and not options.

Assumptions about riskless assets

• Constant Risk-Free Interest rates − Black Scholes model assumes an option where the interest rates paid by the underlying stock are constant and risk-free. However, this is hard to find in the real world.

Assumptions about the option

• The Black Scholes model is almost always equally applicable to American options although it was originally meant for European options. However, the model can be inapplicable in the case of some American put and some calls of dividend-paying stocks.

Assumptions about the market

• No transaction costs − The Black Scholes model assumes that there is no transaction or premium costs of an option. This is also applicable to trades, and bid-ask spreads. This, however, is not applicable in real-world situations as the price of owning an option varies with markets and around the economies.

• Perfectly Liquid Markets − Apart from a market being efficient, The Black Scholes model requires the markets to be completely liquid. That is any quantity of stocks must be possible to be sold anytime in the markets without having to wait for maturity.

• Short-selling is possible − Traders of options should be able to short-sell them making it possible for any option to be sold anytime in the markets. This is a quality of American options as they can be sold anytime instead of European options that can only be sold after maturity.

• No Arbitrage − There would be no arbitrage associated with options trading. That is no such position can be created that would have zero risk and expected return greater than the return on riskless assets.