JavaScript Finance: Profit probability calculator for iron condor

Imagine this: you’re staring at your trading dashboard, analyzing an iron condor options strategy you’ve just set up. The potential for profit looks promising, but the market is unpredictable. You start asking yourself—what are the actual odds of success? How much risk am I really taking on? These aren’t just theoretical questions; they’re the difference between a calculated trade and a reckless gamble.

In this article, we’ll dive deep into building a JavaScript function to calculate the profit or loss of an iron condor strategy at a given stock price and estimate the probability of achieving maximum profit or loss. But before we jump into the code, let’s unpack what an iron condor is, why it’s a popular strategy, and the math behind it. By the end, you’ll not only have a working function but also a solid understanding of the mechanics driving it.

What is an Iron Condor?

An iron condor is a popular options trading strategy designed to profit from low volatility. It involves selling an out-of-the-money (OTM) call and put option while simultaneously buying further OTM call and put options to limit risk. The result is a strategy with defined maximum profit and loss, making it appealing to traders who want to cap their risk exposure.

The payoff diagram for an iron condor resembles a flat plateau in the middle (maximum profit zone) and steep slopes on either side (loss zones). The goal is for the stock price to stay within the range of the short strikes at expiration, allowing all options to expire worthless and capturing the premium as profit.

Breaking Down the Problem

To calculate profit probability for an iron condor, we need to address two key questions:

1. What is the profit or loss at a given stock price?
2. What is the probability of achieving maximum profit or loss?

Answering these requires a mix of basic options math and probability theory. Let’s tackle them step by step.

1. Calculating Profit or Loss

The profit or loss of an iron condor depends on the relationship between the stock price and the strike prices of the options. Here’s how it works:

• Maximum Profit: This occurs when the stock price stays between the short call and short put strikes at expiration. In this case, all options expire worthless, and you keep the net premium collected.
• Maximum Loss: This happens when the stock price moves beyond the long call or long put strikes. The loss is limited to the difference between the strikes of the long and short options, minus the premium collected.
• Intermediate Scenarios: If the stock price lands between the short and long strikes, the profit or loss is calculated based on the intrinsic value of the options.

2. Estimating Probability

To estimate the probability of achieving maximum profit or loss, we use the cumulative distribution function (CDF) of the normal distribution. This requires inputs like volatility, time to expiration, and the relationship between the stock price and strike prices.