Do traders use Black-Scholes-Merton (BSM) model for trading options? Most of them do not. But these are traders whose judgement is shaped by their experience. If you are a novice trader in the options market, you need a tool to substitute for experience. The BSM model can be one such tool. This week, we discuss how to apply the BSM model for trading options despite its limitations.

Issues, applications

As with any model in finance, the BSM model makes assumptions that do not necessarily hold in real-world markets. Suffice it to understand that one such assumption is about volatility being constant. Constant volatility does not mean that an underlying will change by the same amount over any trading period. Rather, the model assumes that changes in volatility has a constant relationship with time.

The argument is based on variance (which is square of volatility) being proportion to time. That is, if the variance of an underlying is 10 per cent for one year, then it ought to be 20 per cent for two years and so on. Standard deviation, which is the square root of variance is, therefore, proportion to square-root of time. And standard deviation is the measure of volatility. Therefore, volatility is assumed is said to be proportion to square-root of time.

This assumption is a problem in real world markets because an asset’s volatility today is dependent on its volatility yesterday. So, if today’s volatility is high, it is highly likely that tomorrow’s volatility will also be high. This will continue until a major event shocks the market and volatility levels change. Therefore, volatility is said to cluster.

The implication is huge. The BSM misprices options because volatility is the primary driver of option prices. That means you cannot compare an option value determined by a model with the actual price of the option traded on the NSE and conclude that the option price is either underpriced or overpriced. That is why you should apply a relative approach. That is, you should not use the BSM model to find whether an option is absolutely cheap or rich (the term used in the market for overpriced options). Rather, you should analyse how cheap or rich one strike is compared to others for the same maturity for the same underlying.

The logic is simple. We know that the BSM model misprices options. But it ought to misprice options in the same way for all strikes on the same underlying for the same maturity. So, comparing the strikes should tell you which strike is cheap or rich compared to the others, despite the limitations of the model. Hence, the implied volatility rule for buying options and the reverse implied volatility rule for shorting options.

So, if you are a novice trader in the options market, using the implied volatility rule applying the BSM model can substitute for the judgment that experienced traders use to choose strikes.

Optional reading

The assumptions of the BSM model is primary reason why you should apply implied volatility of the option, and not the volatility of the underlying. Logically therefore, you should also use the implied option Greeks to fine-tune your trading strategies. That is, you should apply option Greeks such as delta, gamma and theta based on the actual price of the option, and not use Greeks based on the option value using historical volatility.

This helps in fine-tuning your trading strategies. For instance, the BSM model helps you “fix” the at-the-money (ATM) option by indicating the strike whose implied delta is close to 0.50. This helps in setting up short positions, as theta (time decay) drives profit for short options, especially, during the expiry week. True, the BSM model overprices ATM options when volatility declines and underprices ATM options when volatility increases. The model has its uses, despite its limitations.

The author offers training programmes for individuals to manage their personal investments

Related Topics
comment COMMENT NOW