Black-Scholes Explained

A call lets you buy later at a price fixed today. A put lets you sell later at a price fixed today. This screen prices that right. Edit any value, or type a command below.

Inputs

Type
what it trades at now
₹
the price on your ticket
₹
until the ticket expires
d
how jumpy, per year
%
safe-money rate, per year
%
cash paid out, per year
%

Examples

Price

real value right now
hope value (time value)
chance it pays
call / put, same strike

Dials

Chart

Hover or drag across the chart to read a price.

━━ worth today╌╌ worth at expiry┆ underlying price┆ strike● you are here

How the price is built

Formula and where it goes wrong 
d1 = [ ln(S/K) + (r − q + σ²/2) × T ] / (σ × √T)
d2 = d1 − σ × √T

Call = S × e^(−qT) × N(d1)  −  K × e^(−rT) × N(d2)
Put  = K × e^(−rT) × N(−d2) −  S × e^(−qT) × N(−d1)

S underlying price · K strike · T years left · σ volatility · r interest · q dividends · e^(−rT) shrinks a future rupee to today · N( ) chance from the bell curve

  • One volatility for every strike. Real far-away puts cost more than this page shows.
  • Smooth moves only. Real crashes jump past your strike.
  • Volatility never changes here. In a panic it rises, and so does your put. Try F3.
  • Used only at expiry. That fits index options like NIFTY.
  • No trading costs. Far-month options can have wide gaps between buy and sell.