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European Option Price With Normal Approximation

Estimate European call and put values under constant volatility, continuous dividends, and a captured normal-CDF approximation.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

With stock and strike both 100, one year to expiry, 20% annual volatility and zero interest and dividends, the approximate European call and put values are both 7.96557.

d1=[ln(S/K)+(r−q+σ²/2)T]/(σ√T); d2=d1−σ√T; call=Se^(−qT)N(d1)−Ke^(−rT)N(d2); put follows put-call parity.

Worked example

Enter these known values and leave the other values blank.

Current stock price
100 USD
Strike price
100 USD
Risk-free interest rate
0 %
Dividend yield
0 %
Volatility
20 %
Time to maturity
1 yrs
Call option price
7.97 USD
Put option price
7.97 USD

Assumptions and limitations

  • Assume European exercise, constant positive volatility, continuous dividend yield, no transaction costs, and a lognormal underlying. This does not model American early exercise or changing volatility.
  • The source helper named erf is actually a normal CDF approximation. Its two polynomial ranges and clipped tails beyond |d|>6 are translated to decimal arithmetic; this is an approximation, not the mathematical error function.
  • Use one currency throughout. Retained currency selector factors are a historical snapshot, not live exchange rates.
  • Clear an editable unknown before solving an inverse. Selection controls and forced outputs cannot be inferred.

Common questions

What does this model assume?

Assume European exercise, constant positive volatility, continuous dividend yield, no transaction costs, and a lognormal underlying. This does not model American early exercise or changing volatility.

Can I use the currency menu as a current quote?

No. Keep amounts in one currency; conversion factors are a captured historical snapshot.

References

The calculation follows this reviewed mathematical model: d1=[ln(S/K)+(r−q+σ²/2)T]/(σ√T); d2=d1−σ√T; call=Se^(−qT)N(d1)−Ke^(−rT)N(d2); put follows put-call parity. Required model inputs: Underlying price must be positive. Strike price must be positive. Volatility must be positive. Time to expiration must be positive.

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