Option Calculator

# Option Calculator A Black-Scholes option pricing toolkit that runs entirely in your terminal. Feed it a spot price, strike, volatility, and time to expiration — it returns theoretical prices, Greeks, implied volatility, payoff tables, and more. All math is computed inline via Python 3 using the Abramowitz & Stegun approximation for the normal CDF (no scipy dependency). ## Commands ### `price` ``` option-calculator price <type> <spot> <strike> <rate> <vol> <days> ``` Compute the Black-Scholes theoretical price for a European call or put. | Argument | Description | |----------|-------------| | `type` | `call` or `put` | | `spot` | Current underlying price | | `strike` | Strike price | | `rate` | Risk-free rate (annualized, e.g. `0.05`) | | `vol` | Implied volatility (annualized, e.g. `0.20`) | | `days` | Days to expiration | ### `greeks` ``` option-calculator greeks <type> <spot> <strike> <rate> <vol> <days> ``` Compute the five standard Greeks: Delta, Gamma, Theta (per day), Vega (per 1% vol move), and Rho (per 1% rate move). Same arguments as `price`. ### `iv` ``` option-calculator iv <type> <spot> <strike> <rate> <days> <market_price> ``` Back out the implied volatility from a known market price using Newton-Raphson iteration. Converges to 1e-8 precision within 200 iterations. | Argument | Description | |----------|-------------| | `market_price` | The observed option premium | ### `payoff` ``` option-calculator payoff <type> <strike> <premium> [range] ``` Print a table showing intrinsic value and net P/L at expiration across a range of underlying prices. Default range is ±20 around the strike. ### `compare` ``` option-calculator compare <spot> <strike1> <strike2> <vol> <days> ``` Side-by-side comparison of two strikes — call price, put price, deltas, and gamma. Uses a fixed risk-free rate of 5%. ### `chain` ``` option-calculator chain <spot> <vol> <days> ``` Generate a full option chain with calls, puts, deltas, and gamma across strikes from ~80% to ~120% of spot. Each row is flagged as ITM, ATM, or OTM relative to the call side. ### `pnl` ``` option-calculator pnl <type> <entry> <current> <qty> ``` Calculate profit or loss on an existing position. Assumes standard 100 shares per contract. Use negative `qty` for short positions. ### `breakeven` ``` option-calculator breakeven <type> <strike> <premium> ``` Compute the breakeven underlying price at expiration and show max loss for the buyer. ### `help` ``` option-calculator help ``` Print the built-in usage guide. ### `version` ``` option-calculator version ``` Print the current version string. ## Examples ```bash # Price a 30-day call: spot=100, strike=105, rate=5%, vol=20% $ option-calculator price call 100 105 0.05 0.20 30 Black-Scholes Price (call): 0.7677 # Greeks for a 60-day put: spot=50, strike=48, rate=3%, vol=35% $ option-calculator greeks put 50 48 0.03 0.35 60 Greeks (put) S=50 K=48 r=0.03 σ=0.35 T=60d ────────────────────────────────── Delta: -0.312245 Gamma: 0.052040 Theta: -0.020369 (per day) Vega: 0.074853 (per 1% vol) Rho: -0.029259 (per 1% rate) # Solve implied volatility from a market price of 3.50 $ option-calculator iv call 100 105 0.05 30 3.50 Implied Volatility Solver (call) S=100 K=105 r=0.05 T=30d Market=3.50 ────────────────────────────────── Implied Volatility: 0.416566 (41.66%) # Payoff table for a call, strike=100, premium=5.50 $ option-calculator payoff call 100 5.50 Payoff Table (call) K=100 Premium=5.50 ────────────────────────────────── Underlying Intrinsic Net P/L ------------------------------------ 80.00 0.00 -5.50 85.00 0.00 -5.50 ... 100.00 0.00 -5.50 <-- strike 105.00 5.00 -0.50 106.00 6.00 +0.50 110.00 10.00 +4.50 120.00 20.00 +14.50 # Compare two strikes $ option-calculator compare 100 95 110 0.25 45 Strike Comparison S=100 K1=95 vs K2=110 σ=0.25 T=45d ────────────────────────────────── Strike 95.0 Strike 110.0 ------------------------------------------------ Call Price 7.0150 0.7353 Put Price 1.4312 10.0593 Call Delta +0.793714 +0.135799 Put Delta -0.206286 -0.864201 Gamma 0.035611 0.028346 Spot: 100.0 | Rate: 0.05 | Vol: 0.25 | Days: 45.0 # Generate an option chain $ option-calculator chain 100 0.25 45 Option Chain | Spot: 100.0 | Vol: 25% | Days: 45 | Rate: 0.05 Strike Call C.Delta Put P.Delta Gamma IV flag -------------------------------------------------------------- 90.00 10.7823 +0.9268 0.2279 -0.0732 0.012463 ITM 93.00 8.1952 +0.8639 0.6229 -0.1361 0.019087 ITM 100.00 3.6738 +0.5580 3.0651 -0.4420 0.032208 ATM ... 110.00 0.8916 +0.1623 10.2497 -0.8377 0.019938 OTM ... 110.00 0.8916 +0.1623 10.2497 -0.8377 0.019938 OTM # P/L on a long position: bought 5 call contracts at 3.20, now worth 4.80 $ option-calculator pnl call 3.20 4.80 5 Position P/L ────────────────────────────────── Position: Long 5x call Entry: 3.2000 Current: 4.8000 P/L per contract: +1.6000 Total P/L: +800.00 (+50.00%) # Breakeven for a put $ option-calculator breakeven put 100 4.50 Breakeven Analysis ────────────────────────────────── Put Breakeven: 95.5000 Strike (100.00) - Premium (4.5000) Underlying must fall below 95.5000 to profit at expiration. Max loss (buyer): 4.5000 per share ``` ## Configuration The data directory defaults to `$HOME/.option-calculator/`. It stores a `history.log` file that records each `price` command you run for later reference. Override the directory by setting the `OPTION_CALCULATOR_DIR` environment variable before invoking the tool: ```bash export OPTION_CALCULATOR_DIR="/tmp/my-options" ``` ## Data Storage | File | Purpose | |------|---------| | `$HOME/.option-calculator/history.log` | Append-only log of pricing commands and results | The directory is created automatically on first run. ## Requirements - **bash** 4.0+ - **python3** (standard library only — `math` module) - No third-party Python packages needed ## When to Use - Pricing a European option before placing a trade - Checking how Greeks shift across different strikes or expirations - Backing out implied volatility from a quoted premium - Comparing strikes to decide which contract to buy/sell - Generating a quick option chain for scenario analysis - Calculating breakeven and P/L on existing positions *Powered by BytesAgain | bytesagain.com | hello@bytesagain.com*