Traders often debate whether short out-of-the-money (OTM) or at-the-money (ATM) puts are riskier. The argument for OTM put options being riskier is that their Speeds (or dGamma/dspot) are higher than the ATMs’ ones, thus the Gamma, which is negative, can increase (in absolute value) substantially during a market downturn.
In this post, we will quantify and compare the risks of short OTM and ATM put options. We do so by performing Monte Carlo simulations and calculating the Value at Risk (VaR at 95% confidence interval) and variance of the return distribution. This strategy involves shorting unhedged puts. The return is determined as follows,
where P_{t0} and P_{T} denote the put prices at time zero and expiration respectively
K is the strike price; K=90, 100 for OTM and ATM options, respectively
m is a factor for margin. m=100% means that we sell a cash-secured put.
Note that the above equation takes into account the margin requirement in an approximate way. The exact formula for margin calculation depends on brokers, exchanges and countries. But we believe that using a more realistic margin calculation formula will not change the conclusion of this article.
We use the same simulation methodology and parameters as in the previous post. The parameters are as follows,
Parameter | Value |
Initial stock price | 100 |
Volatility | 20% |
Risk-free rate | 0.02 |
Drift | 0.07 |
Days in simulation | 252 |
Time step (day) | 1d |
Number of paths | 10000 |
Model | GBM |
It’s important to note that we focus here on the risks only. Hence we utilize the same values for the option’s implied volatility and the underlying’s realized volatility. In real life the puts implied volatilities are usually higher than the realized due to volatility and skew risk premia. This means that the strategy’s real-life expected return is normally higher. Our simulated return is more conservative.
The table below summarizes the risk characteristics of short put options.
ATM (K=100) | OTM (K=90) | |||||
Leverage | Return | Variance | VaR | Return | Variance | VaR |
100% | 0.0171 | 0.0075 | 0.1940 | 0.0118 | 0.0031 | 0.1303 |
50% | 0.0370 | 0.0292 | 0.3844 | 0.0206 | 0.0133 | 0.2783 |
15% | 0.1317 | 0.3155 | 1.2589 | 0.0679 | 0.1502 | 0.9339 |
We observe that for the same level of leverage, short OTM put positions are actually less risky than the ATM ones. For example, for m=100%, i.e. a cash-secured short put position, the variance and VaR of the OTM position are 0.0031 and 0.1303 respectively; they are smaller than the ATM option’s counterparts which are 0.0075 and 0.1940, respectively.
The risk comes from leverage. Let’s say, for example, a trader wants to sell OTM puts. Since he receives less premium for each put sold, he will likely increase the position size. For example, if he sells 2 OTM puts using leverage (m=50%), then the variance and VaR of his position are 0.0133 and 0.2783 respectively. Compared to selling 1 ATM cash-secured put, the risks increased substantially (VaR went from 0.194 to 0.2783)
In summary, ceteris paribus, a short OTM put option position is less risky than the ATM one. The danger arises when traders use excessive leverage.