How does Shoals price options?

Shoals uses a 128-step Cox-Ross-Rubinstein (CRR) binomial tree with Broadie-Detemple smoothing for American option pricing. The tree incorporates term-structure volatility, moneyness skew, and discrete dividend adjustments. Stock prices follow geometric Brownian motion with optional Merton jump diffusion and Heston stochastic volatility.

What are the option Greeks?

The Greeks measure an option's sensitivity to different factors. Delta measures price sensitivity to the underlying stock. Gamma measures the rate of change of delta. Theta measures time decay. Vega measures sensitivity to volatility changes. Rho measures sensitivity to interest rate changes. Shoals displays all five Greeks in real time across a 25-strike options chain.

What is the Heston stochastic volatility model?

The Heston model treats volatility as a random process that mean-reverts over time, rather than being constant as in Black-Scholes. This produces realistic volatility clustering (periods of high and low volatility) and a non-flat implied volatility surface. Shoals implements Heston with configurable mean reversion speed, long-run variance, and volatility of volatility.

What market events does Shoals simulate?

The narrative event engine includes over 400 curated scenarios: earnings surprises, Federal Reserve rate decisions, geopolitical events, sector rotations, and black swan events. Each event modifies the underlying price process parameters (drift, volatility, jump intensity) to produce realistic market dynamics and test portfolio resilience.

How do I build a multi-leg options strategy in Shoals?

Click the options chain to add individual legs, then switch to the Strategy tab to see the combined payoff diagram, Greek overlays, max profit/loss, and break-even prices. Shoals supports any combination of calls and puts at different strikes and expirations.

Does Shoals collect any personal data?

No. Shoals runs entirely in your browser with no server-side processing, no cookies, and no analytics tracking. All simulation state stays on your device.

Is Shoals free and open source?

Yes. Shoals is licensed under AGPL-3.0 and the source code is available on GitHub. It is free to use for educational and personal purposes.

What is implied volatility?

Implied volatility is the market's forecast of a likely movement in an asset's price, derived by reverse-engineering the Black-Scholes model from observed option prices. In Shoals, the vol surface adjusts implied volatility by moneyness and time to expiration, creating a realistic volatility smile. Options far from the money or near expiration trade at different implied vols than at-the-money options.

Shoals — Interactive Options Trading Simulator

What is Shoals?

Shoals is an options trading simulator that models derivatives pricing under realistic market conditions. Stock prices evolve with stochastic volatility and jump diffusion while a narrative event engine introduces market shocks, connecting abstract pricing theory to real-world dynamics.

Pricing Models

The underlying stock follows geometric Brownian motion with optional Merton jump diffusion (sudden large moves) and Heston stochastic volatility (time-varying vol that mean-reverts). Interest rates follow a Vasicek process. American options are priced on a 128-step CRR binomial tree with term-structure volatility and moneyness skew adjustments.

Strategy Builder

The multi-leg strategy builder supports spreads, straddles, strangles, condors, butterflies, and custom combinations. Each strategy displays a payoff diagram, Greek overlays showing how sensitivity changes across strikes, maximum profit and loss, and break-even points. A margin system tracks portfolio-level exposure and buying power.

Market Events

Over 400 narrative scenarios — earnings surprises, central bank decisions, geopolitical crises, and sector rotations — modify the price process in real time. Events change drift, volatility, and jump intensity, forcing traders to adapt strategies to evolving conditions rather than static assumptions.

Price Impact

Shoals uses the Almgren-Chriss model to simulate price impact from large trades. Buying or selling significant quantities moves the stock price against the trader, with impact decaying over time. This creates realistic market microstructure effects and forces traders to consider execution strategy, not just option selection.

Narrative Framework

The simulation is set at Meridian Capital during the Barron administration. Over 400 narrative market events are not random: they follow storylines with followup chains, political consequences, and faction dynamics. The game tracks twelve character traits and six faction standings that shape which events occur and how they resolve, culminating in one of six ending types with a five-page adaptive epilogue.

Accessibility

Shoals supports keyboard navigation for all controls and dialogs, high-contrast mode via the theme toggle, and ARIA labels on interactive elements. Chart data is accessible through the numerical sidebar displays. All popup dialogs are focus-trapped. No flashing content or motion simulation hazards.

See also: Geon for particle physics, Cyano for cellular metabolism, Gerry for electoral fairness.

Learning Outcomes

After using Shoals, students should be able to: derive the Black-Scholes price for a European call and put; explain why American options require numerical methods like the binomial tree; describe how stochastic volatility (Heston model) produces volatility smiles that geometric Brownian motion cannot; compute and interpret delta, gamma, theta, vega, and rho for single options and multi-leg strategies; and analyze how market events propagate through the Greeks to affect portfolio value.

Prerequisites

Basic probability and statistics (expected value, standard deviation, normal distribution). Familiarity with compound interest and present value. No prior knowledge of options or derivatives is required.

Volatility Surface

The implied volatility surface in Shoals plots IV across strike prices and expirations. Under GBM, the surface is flat — IV equals realized volatility everywhere. Under Heston, the surface develops a characteristic skew (lower strikes have higher IV) and term structure (short-dated options show more curvature). The event engine creates temporary surface dislocations that mean-revert over time, mimicking real market behavior around earnings and macro announcements.

References

F. Black and M. Scholes, "The Pricing of Options and Corporate Liabilities" (1973). S. L. Heston, "A Closed-Form Solution for Options with Stochastic Volatility" (1993). J. C. Cox, S. A. Ross, and M. Rubinstein, "Option pricing: A simplified approach" (1979).