Black-Scholes Model

The Black-Scholes Model calculates ticket prices based on the Black-Scholes option pricing model. This method uses financial market data to estimate the fair price of options, which are then mapped to ticket prices. Key components include the current asset price, volatility of returns, time until option expiration, and the risk-free interest rate.

Here is a brief explanation of each variable used in the Black-Scholes model:

1. Data Preparation: The model establishes a range of potential strike prices for options, based on the underlying asset's current price, adjusted by a specified step size.

2. Volatility Calculation (σ): Annualized volatility is computed using the standard deviation of the asset’s returns, adjusted for the data interval (daily or hourly).

3. Time Adjustment (t): The time until option expiration is normalized to a yearly scale, depending on the data interval.

4. Risk-free Rate (r): A constant risk-free interest rate, such as 0.02 or 2%, is assumed.

Option Price Calculation

Prices for both call and put options are calculated using the Black-Scholes formula. The formulae are:

Intersection Point

The model determines an intersection strike price for the optimal switch from call to put option pricing.

Normalization and Adjustment

Resulting option prices are normalized and adjusted to fit within a specified price range, such as 0 to 10 units.