Options Prediction Calculator

Black-Scholes Formula for Call Options:

\[ C = S \times e^{-qT} N(d_1) - K \times e^{-rT} N(d_2) \] \[ d_1 = \frac{\ln(S/K) + (r - q + \sigma^2/2)T}{\sigma\sqrt{T}} \] \[ d_2 = d_1 - \sigma\sqrt{T} \]

Stock Price (S):

currency

Strike Price (K):

currency

Risk-Free Rate (r):

decimal

Dividend Yield (q):

decimal

Time to Maturity (T):

years

Volatility (σ):

decimal

Call Option Price:

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1. What is the Black-Scholes Model?

The Black-Scholes model is a mathematical model for pricing options contracts. It calculates the theoretical price of European-style options using current stock price, strike price, time to expiration, risk-free rate, and volatility.

2. How Does the Calculator Work?

The calculator uses the Black-Scholes formula for call options:

\[ C = S \times e^{-qT} N(d_1) - K \times e^{-rT} N(d_2) \] \[ d_1 = \frac{\ln(S/K) + (r - q + \sigma^2/2)T}{\sigma\sqrt{T}} \] \[ d_2 = d_1 - \sigma\sqrt{T} \]

Where:

\( S \) — Current stock price
\( K \) — Strike price
\( r \) — Risk-free interest rate
\( q \) — Dividend yield
\( T \) — Time to expiration (in years)
\( \sigma \) — Volatility of the stock
\( N() \) — Cumulative standard normal distribution

Explanation: The formula calculates the fair value of a call option based on the probability-weighted present value of the option's payoff at expiration.

3. Importance of Option Pricing

Details: Accurate option pricing is crucial for traders, investors, and financial institutions to make informed decisions about buying, selling, or hedging options positions.

4. Using the Calculator

Tips: Enter all required parameters in the specified units. Stock and strike prices should be in the same currency. Rates and volatility should be entered as decimals (e.g., 5% = 0.05).

5. Frequently Asked Questions (FAQ)

Q1: What assumptions does the Black-Scholes model make?
A: The model assumes lognormal distribution of stock prices, no dividends (unless modified), no transaction costs, constant volatility, and the ability to continuously hedge.

Q2: Does this work for American options?
A: This calculator is for European options only. American options require more complex models due to early exercise features.

Q3: What's a typical volatility value?
A: Volatility typically ranges from 0.2 (20%) for stable stocks to 0.6 (60%) or more for highly volatile stocks.

Q4: How does dividend yield affect option price?
A: Higher dividend yields decrease call prices (and increase put prices) since dividends reduce the expected stock price.

Q5: What are the limitations of Black-Scholes?
A: It doesn't account for large jumps in stock prices, changing volatility (volatility smile), or interest rate changes during the option's life.