Black-Scholes model assumptions

The assumptions of this Option pricing formula are covered below, with my own comments.

1. Interest rate is known and constant throughout time Link to heading

This is not a bad or unrealistic assumption. After all the base interest rate is set by the Central Bank, while the actual reference rate used to price the option is also known or doesn’t change that dramatically (sort of) over the lifetime of the option, i.e. LIBOR, EURIBOR, etc.

2. Stock price follows a random walk and the variance follows a log-normal distribution Link to heading

This is the assumption that I have the most problem with and the one I will need to test. The claim that stock prices follow a random walk can hardly be justified by looking at real world data. No one really knows if a stock will go higher or lower on short horizons, i.e. daily, but then to claim its return distribution can be approximated by a normal distribution, and in that turn makes prices log-normal, is a stretch.

3. Volatility is constant Link to heading

This is arguably the most problematic assumption, but adjustments have been introduced to incorporate non-constant volatility. Volatility is not constant and not known in advance, after all.

4. Assumptions about the option and the market Link to heading

A host of other assumptions are made, like fractional shares allowed, no restrictions on short selling, stock doesn’t pay a dividend, no transaction costs, no arbitrage, etc.

A lot of these assumptions make sense and are sensible, while others can be adjusted, like incorporating divvies, or adjusting for transaction costs based on the actual market the option is traded, etc., so won’t spend much time on these.