T2W Trading Community

Calculating the Probabilities of a Spread

Before an insurance company issues a policy, they compile several pieces of data describing the individual seeking coverage. They use this information to determine the likelihood of a claim and its potential magnitude. After doing so they will conclude on a fair premium. Similarly, when constructing a credit spread strategy it is important to identify the prospects of incurring a loss, and knowing the extent of the damages.

The first step is to determine the odds of the options expiring [[in–the-money option|in-the-money]]. Obviously, the less likely it is to be profitable to the buyer, the more desirable it is for the seller. Traders can easily estimate the probabilities of a credit spread by calculating the delta of each option. The delta is equal to the change in the option value for each unit of change in the underlying futures contract. The delta can be considered an estimate of the chances that a particular option will expire in the money. For example, an-at-the-money option typically has a delta of 0.50. In other words there is a 50% chance that the underlying contract will be trading favorable to the option’s strike price at expiration.

The prospects for the sale of a credit spread yielding the maximum loss can be figured by multiplying the deltas. Going back to the previous illustration, if you sold a Dow 10300 call option with a delta of 0.30 and bought the 10500 with a delta of 0.15 for protection the probability of the market trading over 10500 is only 15% at the time of the trade. This is the worst-case scenario for the seller resulting in a $1,600 loss.

Likewise, given the theoretical delta values, a seller of this spread would avoid the maximum loss 85 % of the time and would collect the entire premium roughly 70% (1.00 – 0.30) of the time. If the market goes against your position, you could mitigate losses by putting on another credit spread with higher strike prices. The premium collected from the 2nd position will help to offset the loss of the original trade.

Conclusion

The probabilities of options trading are not so different from those used in the casino industry. While there are 'jackpots' to be paid, over time the expected outcome is always in favor of the house. A simple stroll down the Las Vegas Strip proves that in the long run...it pays to play the odds.