About OptionsMath

OptionsMath is a free library of options trading calculators — single-leg call and put profit and loss, vertical spreads, iron condors, butterflies, straddles and strangles, covered calls and protective puts, calendar and diagonal spreads, Black-Scholes theoretical pricing, the Greeks, implied volatility, option rolls, expected move, probability of profit, and position sizing. No signups, no paywalls, no data collection. Just the tools and context you need to model a trade before you put real money behind it.

A brief history

OptionsMath grew out of the same calculator-building habit that started AJ Designer in the early 2000s. I had been writing physics and engineering calculators for years when I started trading options for my own account, and I quickly discovered that most of the payoff and pricing tools online were either locked behind a broker login, buried in a desktop platform, or wrapped in a sales pitch for a trading service. I wanted clean, focused calculators I could link to from my own notes — and so did a lot of other people.

The site started small with a call and put profit/loss calculator and a Black-Scholes pricer, and grew from there as I added the common spreads, the income strategies, the volatility tools, and the position-management calculators. Many of the pages on this site exist because a reader emailed and asked if I could add a particular strategy or scenario.

How the math is verified

Every calculator is grounded in established options-pricing references — Hull's Options, Futures, and Other Derivatives, Natenberg's Option Volatility and Pricing, and Hoadley's well-known options analytics documentation. Payoff formulas are derived from the textbook per-leg intrinsic values; theoretical prices and Greeks are implemented from the standard Black-Scholes-Merton equations and cross-checked against textbook benchmarks at known input sets.

Every calculator ships with numeric assertion tests that pin the formulas to known answers, so a refactor that breaks the math fails the build instead of silently shipping a wrong number. I also rely heavily on bug reports and correction suggestions from readers — traders, students, and quants who spot an off-by-one in a spread payoff, a missing edge case in a roll calculation, or a place where the assumptions need to be stated more clearly. Those reports have caught real mistakes, and reader feedback is one of the most valuable forms of review this site gets. If you find an error, please email me — I'd rather fix it than defend it.

A note on appropriate use

OptionsMath is built for education, scenario modeling, and first-pass analysis. The calculators are not investment advice, and they don't account for commissions, fees, hard-to-borrow costs, early assignment on American-style options, dividend timing, pin risk at expiration, or the dozens of other real-world frictions that affect actual P/L. Theoretical prices and Greeks assume a frictionless Black-Scholes world that does not exist. For any real trade, confirm the numbers against your broker's platform and decide based on your own risk tolerance, account constraints, and regulatory situation.

About the author

Hi, I'm Jimmy Raymond. I started building calculators while working through problems in school at New Mexico Tech and the University of New Mexico, where I earned a B.S. in Environmental Engineering and a B.S. in Computer Science. The two degrees are what made sites like this one possible — engineering gave me the dimensional-analysis and applied-math foundation, and computer science gave me the tools to turn equations into software that someone else can pick up and use in thirty seconds. That's an uncommon combination: most CS programs don't require classical mechanics, thermodynamics, fluid statics, or rigorous dimensional analysis, and most engineering programs don't cover the algorithms, testing methodology, and production-software practice that CS programs do. Both sides matter for a calculator that has to produce a number you'll act on.

In the years since, my professional work has taken me through safety-critical aircraft and space systems, real-time embedded software, and full-stack web development. That discipline shapes how the calculators on OptionsMath are built: each payoff formula is pinned to an options-textbook source, each solver has automated tests that compare its output to known answers across strikes and expiration scenarios, and every change runs through a regression suite before it ships. None of that substitutes for your own due diligence, which is why every result page is framed as an educational estimate, not financial advice.

I trade options for my own account, which is how most of the calculators on this site got prioritized — these are the tools I actually use to think through a trade before I put it on. I'm based in Albuquerque, New Mexico.

Contact

Email me at aj@ajdesigner.com for corrections, calculator requests, or general feedback. You can also find me on LinkedIn.

— Jimmy