Heston Put Option Price Calculator

The Heston put option price calculator estimates the value of a put option using the Heston model, which accounts for stochastic volatility. This model is more sophisticated than the Black-Scholes model as it allows volatility to change over time.

How to use this calculator

To calculate the Heston put option price, enter the following parameters:

Current stock price (S)
Strike price (K)
Time to maturity (T) in years
Risk-free interest rate (r)
Long-term variance (σ²)
Volatility of volatility (ω)
Mean reversion speed (κ)
Correlation (ρ)

Click "Calculate" to see the estimated put option price. The calculator will display the result along with a chart showing the option price over time.

Formula and assumptions

The Heston model calculates the put option price using the following formula:

Put Option Price = N(-d₂) * K * e^(-rT) - N(-d₁) * S₀

Where:

N(x) is the cumulative standard normal distribution
d₁ = (ln(S₀/K) + (r + σ²/2)T) / (σ√T)
d₂ = d₁ - σ√T

The Heston model makes several key assumptions:

Volatility is stochastic and follows a mean-reverting process
The stock price follows a geometric Brownian motion
There are no dividends or transaction costs
The market is efficient and frictionless

Worked example

Let's calculate the put option price for the following parameters:

Parameter	Value
Current stock price (S₀)	$100
Strike price (K)	$105
Time to maturity (T)	1 year
Risk-free rate (r)	5%
Long-term variance (σ²)	0.04
Volatility of volatility (ω)	0.5
Mean reversion speed (κ)	1.5
Correlation (ρ)	0.3

Using these values, the calculator estimates the put option price to be approximately $5.23.

Interpreting results

The put option price represents the value of the put option contract. A higher price indicates that the option is more valuable, which typically occurs when:

The stock price is expected to fall
The time to maturity is longer
The volatility is higher
The risk-free interest rate is lower

When interpreting the results, consider the following:

The Heston model provides a more accurate estimate of option prices than the Black-Scholes model, especially for options with longer maturities or higher volatility.

FAQ

What is the Heston model?: The Heston model is a stochastic volatility model that extends the Black-Scholes model by allowing volatility to change over time. It provides more accurate option pricing for certain types of options.
How does stochastic volatility affect option pricing?: Stochastic volatility accounts for the fact that volatility can change over time, which can lead to more accurate option prices, especially for options with longer maturities.
What are the limitations of the Heston model?: The Heston model assumes that volatility follows a mean-reverting process and that the stock price follows a geometric Brownian motion. These assumptions may not hold in all market conditions.
How can I use the Heston put option price calculator?: Enter the current stock price, strike price, time to maturity, risk-free interest rate, long-term variance, volatility of volatility, mean reversion speed, and correlation. Click "Calculate" to see the estimated put option price.
Is the Heston model suitable for all types of options?: The Heston model is particularly suitable for options with longer maturities or higher volatility. For options with shorter maturities or lower volatility, the Black-Scholes model may be more appropriate.