Estimate fair option price limits in seconds today. Enter spot, strike, rates, dividends, time quickly. See call and put bounds, then export results easily.
This calculator applies classic no-arbitrage bounds for European options under continuous compounding. Let S0 be the spot, K the strike, r the risk-free rate, q the dividend yield, and T time to maturity in years.
These bounds are model-free: they do not assume volatility or a pricing model, only the absence of arbitrage with borrowing/lending at rate r.
| Type | S0 | K | r | q | T | Lower | Upper |
|---|---|---|---|---|---|---|---|
| Call | 100 | 105 | 0.05 | 0.02 | 0.50 | 0.000000 | 99.004983 |
| Put | 100 | 105 | 0.05 | 0.02 | 0.50 | 5.000000 | 102.406016 |
| Call | 250 | 240 | 0.03 | 0.00 | 1.00 | 17.126925 | 250.000000 |
Example bounds are illustrative. Your results update using your inputs.
Option prices should stay inside limits implied by a tradable stock and a risk-free account. When quotes drift outside, a simple long-short strategy can lock in profit without forecasting volatility. Bounds add a fast screening layer for data pipelines, model checks, and teaching demos.
The calculator converts spot and strike into present values using continuous compounding. PV(S)=S0·e^(−qT) adjusts the stock for dividend yield, while PV(K)=K·e^(−rT) discounts the strike at the risk-free rate. These quantities define the tightest model-free interval under frictionless assumptions. In data cleaning, these present values help normalize quotes across maturities and rate environments before deeper model fitting steps.
For a European call, the lower bound is max(0, PV(S)−PV(K)). The call cannot be worth less than discounted intrinsic value because you can replicate that payoff floor with stock and borrowing. The upper bound is PV(S) because owning the discounted stock dominates the call payoff at expiry.
For a European put, the lower bound is max(0, PV(K)−PV(S)). A put cannot trade below discounted intrinsic value since cash and stock can replicate the minimum payoff. The upper bound is PV(K) because the put payoff never exceeds K, so paying more than the discounted strike is dominated by cash. High rates tighten the put interval by reducing PV(K).
If you enter a market price, the tool flags whether it falls inside the interval. Analysts often store bounds next to each quote and highlight violations for review. Many apparent breaches vanish after fixing dividend assumptions, rate conventions, or stale data timestamps. Persistent breaches can indicate misquotes or arbitrage pressure. Use bid and ask separately to avoid mixing spreads.
CSV export supports spreadsheets and batch audits, while the PDF snapshot is useful for sharing one computation. For learning, change one input at a time and observe the direction: higher r lowers PV(K), higher q lowers PV(S), and longer T increases the discount impact. This behavior helps sanity-check large datasets quickly. Combine exports with data sources for traceability.
Frictionless trading, ability to borrow or lend at the risk-free rate, and known dividend yield over the option life. No volatility model is needed.
They strictly describe European exercise. American calls on non-dividend stocks share the same upper bound, but early exercise can change tightness, especially for puts.
Set q to zero for a conservative baseline, then test plausible q values. Dividend assumptions strongly affect PV(S) and therefore both bounds.
If discounted intrinsic value is negative, arbitrage implies the option cannot be priced below zero. Options have limited liability, so the minimum price is zero.
It suggests a potential arbitrage or a data issue. Recheck rates, time units, dividends, and whether the quote is mid, bid, or ask.
Continuous compounding for both r and q. If your inputs are simple annual rates, convert them consistently before entering values.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.