Previously in this column, we mentioned that you can use the Black-Scholes-Merton (BSM) model to trade options. A reader wanted to know if individuals can trade options without applying the BSM model. This week, responding to the reader’s query, we show how you can trade options applying only the liquidity rule.

Change in OI

The BSM model is useful when you want to determine whether an option is trading rich or cheap relative to other strikes for the same underlying and expiration date. For instance, if you want to choose between the 17000, the 17100 and the 17200 next-week Nifty calls, you could use BSM model to determine the implied volatility and then pick the one with the lowest volatility. Note that implied volatility is the output you get when you feed the spot price, the strike price, time to expiry of the option and the option price into the BSM model. The argument behind this application is that we can use the model for relative pricing, not for absolute pricing, given its limitations. But what if you do not want to use the BSM model?

Liquidity is important when you trade European options. This is because you must sell your long positions to take profits, as exercise is not possible until option expiry. So, instead of using the BSM model, you can simply apply the liquidity rule.

Your first step is to focus on at-the-money (ATM), and immediate two out-of-the-money (OTM) strikes. Next, you must pick the one that is most liquid of the three strikes. To do so, look at the strike that has the maximum positive change in open interest (OI). The argument is that both long and short positions must be closed before expiry for traders to take profits or reduce their losses. So, whether a trader is long or short, she must come back to the market before expiry to close her position. So, greater the increase in OI, greater the likelihood that the strike will be liquid.

Directions sans volatility
For a directional view on the underlying with no view on volatility, you can use the liquidity rule without applying the BSM model

As you can see, not applying the BSM model would mean that you are only concerned about liquidity and not the cost that you pay for the option. It most cases, this should not be an issue, as the three strikes would have similar implied volatility. But not applying the BSM model could cut into your profits when you expect volatility to implode before option expiration. Why?

Implied volatility is part of the time value component of the option price. This component drags the option price, as time value must become zero at option expiry. Therefore, buying an option that is rich (higher implied volatility) would mean lower profits or greater losses on the long position when volatility is expected to implode. Most traders often have a directional view on the underlying with no view on volatility. In such cases, you can use the liquidity rule without applying the BSM model.

Optional reading

One of the critical issues with the BSM model is its assumption that volatility is a constant. This is far from how volatility behaves in real-world markets; for, volatility changes over time. Yet, the BSM model is important if you have a view on volatility! This is because we use the model to capture relative value (rich or cheap), not absolute value.

Note that the BSM model is no less important if you intend to set up a short position and expect volatility to implode. In this case, you must choose the strike that has the highest implied volatility to improve the chances of making gains. This is because, gains for short positions in ATM and OTM options come from time decay. And imploding implied volatility accelerates time decay, thereby providing opportunities to close the position sooner if your price target is achieved.

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

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