Fair Value — Nebula Capital Systems

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FAIR VALUE — BASIC & ELITE

Client-side analytical calculators for options pricing and equity valuation. Black-Scholes Greeks, DCF modeling, and margin of safety analysis — all computed locally in your browser.

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INPUTS

UNDERLYING PRICE (S) — $

STRIKE PRICE (K) — $

DAYS TO EXPIRATION (T)

IMPLIED VOLATILITY (σ) — %

RISK-FREE RATE (r) — %

OPTION TYPE

CALL PUT

THEORETICAL PRICE & GREEKS

THEORETICAL PRICE

—

per share (×100 for standard contract)

DELTA (Δ)

—

Price change per $1 underlying move

GAMMA (Γ)

—

Delta change per $1 underlying move

THETA (Θ) — per day

—

Value lost per calendar day

VEGA — per 1% IV

—

Value change per 1% IV move

RHO (ρ) — per 1% rate

—

Value change per 1% rate move

D1 / D2

—

Black-Scholes intermediate values

GREEKS GLOSSARY

Rate of change of option price per $1 move in the underlying asset. A call with delta of 0.50 gains approximately $0.50 in value for each $1 rise in the underlying. Delta ranges from 0 to 1 for calls, and −1 to 0 for puts. At-the-money options have delta near ±0.50.

Rate of change of delta per $1 move in the underlying. High gamma means delta shifts rapidly as price moves — at-the-money options near expiration exhibit the highest gamma. Gamma is always positive for long options.

Rate of time decay — the amount of value an option loses per calendar day, all else equal. Theta is negative for long options and accelerates as expiration approaches. Options lose roughly 1/√T of their remaining value per day.

Sensitivity to implied volatility — the change in option value per 1% move in implied volatility. Longer-dated options have higher vega. A vega of 0.20 means the option gains $0.20 if IV rises 1%. Always positive for long options.

Sensitivity to interest rate changes — the change in option value per 1% move in the risk-free rate. Call options benefit from higher rates (positive rho); puts lose value (negative rho). Rho is most significant for longer-dated options.

DCF INPUTS

CURRENT EPS ($)

EPS GROWTH RATE YEARS 1–5 (%)

EPS GROWTH RATE YEARS 6–10 (%)

TERMINAL GROWTH RATE (%)

DISCOUNT RATE (%)

SHARES OUTSTANDING (MILLIONS)

CURRENT PRICE (OPTIONAL — for margin of safety)

TOTAL INTRINSIC VALUE ($M)

—

INTRINSIC VALUE PER SHARE

MARGIN OF SAFETY

—

DISCOUNTED CASH FLOW — YEAR-BY-YEAR PROJECTION

YEAR	EPS ($)	GROWTH (%)	DISCOUNT FACTOR	PRESENT VALUE ($)

DCF outputs are mathematical models based on user-provided assumptions. They are not investment advice or recommendations, and should not be relied upon for any trading or investment decision. Small changes in assumptions produce large changes in outputs. The terminal value is especially sensitive to growth rate and discount rate inputs. This tool is for educational and analytical purposes only. Nebula Capital Systems is not a registered investment advisor.