Calculator Input Form
Use the grid below. Large screens show three columns. Smaller screens show two. Mobile shows one.
Example Data Table
This sample shows a one period call setup using simple compounding.
| Current Price | Up Price | Down Price | Strike | Rate | Time | p | Call Value |
|---|---|---|---|---|---|---|---|
| 100 | 120 | 90 | 105 | 5% | 1 | 0.500000 | 7.142857 |
Formula Used
1) Up and Down Factors
u = Su / S0
d = Sd / S0
2) Risk Free Growth Factor
For simple compounding:
R = 1 + r × t
For continuous compounding:
R = e^(r × t)
3) Risk Neutral Probability
p = (R - d) / (u - d)
q = 1 - p
4) Expected Payoff and Present Value
Expected Payoff = p × PayoffUp + q × PayoffDown
Option Value = Expected Payoff / R
5) No Arbitrage Check
Sd < S0 × R < Su
If this condition fails, the computed probability may fall outside zero and one.
How to Use This Calculator
- Enter the current asset price.
- Enter the price in the up state.
- Enter the price in the down state.
- Enter the strike price for the option payoff.
- Enter the risk free rate as a percentage.
- Enter the time period used by the model.
- Select simple or continuous compounding.
- Select call or put, then press Calculate Now.
The calculator returns probabilities, option value, hedge ratio, bond position, expected payoff, and a pricing consistency warning.
Frequently Asked Questions
1) What is a risk neutral probability?
It is a pricing probability, not a real world forecast. It forces the asset to grow at the risk free rate inside the pricing model.
2) Why can the probability be outside zero and one?
That usually means your inputs violate the no arbitrage condition. The up and down prices must bracket the risk adjusted future price.
3) What does the calculator discount?
It discounts the expected option payoff by the period growth factor. That gives the present value under the one period binomial model.
4) Should I use simple or continuous compounding?
Use the method that matches your pricing convention. Simple compounding fits many classroom examples. Continuous compounding is common in finance theory.
5) What are u and d in the formula?
They are the up and down factors relative to today’s price. The calculator computes them from the future state prices you enter.
6) Can this page price both calls and puts?
Yes. Choose the option type from the dropdown. The page then computes state payoffs and discounts the risk neutral expected payoff.
7) What does the delta hedge mean?
Delta shows the stock position in the replicating portfolio. Combined with the bond position, it reproduces the option payoff across both states.
8) Why include CSV and PDF downloads?
They make it easier to document scenarios, compare cases, or share pricing outputs with students, clients, or team members.