We have so far discussed how to choose call strikes and why options decline faster than they go up for the same change in the price of the underlying. We also saw how to determine whether to set up a long call position or not. This week, we combine all these arguments and discuss how they relate to put options.

Strategic rules

You would buy a put option when you have a view that the underlying is likely to decline. Your choice of the put strike should be based on the implied volatility rule. That is, you should first select the at-the-money (ATM) strike (one most close to the current spot price), an immediate out-the-money (OTM) strike and an immediate in-the-money (ITM) strike. You should then input the current spot price, the strike price, the time to maturity, the risk-free rate and the last traded price for each of the three options into a Black-Scholes-Merton (BSM) calculator. Then, select the strike with the lowest implied volatility.

For the selected strike, you should also check the change in open interest. A large change in open interest indicates good liquidity. If the change in open interest is insignificant, then select the strike with the next lowest implied volatility.

Before you set up the strategy, determine whether going long on the chosen strike has the potential to generate any significant profit. For this, you should assume that the underlying will reach its target price at the expiry of the option. This is because it is easy to determine the price of the option at expir as it has only intrinsic value and zero time value; all ITM puts will have intrinsic value (strike minus spot) and all OTM options and the ATM option will have zero value at expiry.

You should set up the trade only if the reward-to-risk ratio is at least two-to-one. That is, for every two points of reward, you should not risk more than one-point of your trading capital. Suppose the put you choose trades at 100 points today and the intrinsic value of this strike at expiry is 325 points if the underlying were to reach your price target. The reward is 225 points (325 minus 100) for a risk of 100 points, a reward-to-risk ratio of 2.25.

Finally, note that put Greeks have similar characteristics as call Greeks. That means put options will decline in price more than they will increase in price for a given change in the underlying price. So, put delta and gamma will work in your favour when the underlying goes down (puts go up in price when the underlying declines), with theta working against your position. When the underlying moves up, put delta and theta will work against your position with only gamma working in your favour.

Optional reading

The put delta is denoted by a negative sign because puts move in the opposite direction to the underlying. Suppose an OTM put has a delta of -0.30. This means that the put price will increase by 0.30 point for a one-point decline in the underlying.

The rule for determining the new delta when the underlying changes is the same as with calls; you have to add the gamma to the old delta when the underlying moves up and deduct the gamma from the delta when the underlying declines. So, if the gamma is 0.05 for the above OTM put, new delta will be -0.35 if the underlying declines and -0.25 when the underlying moves up one point. Ignoring the minus sign, you can see that the put delta increases when the underlying moves favourably (price declines) and the delta declines when underlying moves adversely (price increases).

Finally, note that the implied volatility will not be the same for the same strike call and put because demand for these strikes will not be the same.

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