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Option Valuation

What's your option worth?

Apply Black-Scholes to determine fair option prices.

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Purpose of Option Valuation 

Option valuation determines an option's fair price by considering factors that influence its premium. 

While various models, such as the binomial tree model, exist, this lesson will focus on the core concepts rather than the mathematical formulas. 

We'll explore the fundamental ideas behind the Black-Scholes model to understand how variables like asset price, strike price, time, and volatility interact to set an option's value. 

This approach lays the groundwork for informed trading decisions.

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Introduction to the Black-Scholes Model 

The Black-Scholes model is a mathematical formula used to calculate the fair price of European-style call and put options. 

It incorporates the current price of the underlying asset, the option's strike price, time to expiration, risk-free interest rate, and the asset's volatility. 

By integrating these variables, the model delivers a theoretical value for options, allowing traders to evaluate whether an option is fairly priced and make informed trading decisions.

Key Assumptions of the Black-Scholes Model 

The Black-Scholes model relies on assumptions: the underlying asset's returns follow a lognormal distribution, meaning prices cannot be negative and returns are normally distributed. 

Volatility and the risk-free interest rate are constant over the option's life. 

The model assumes no dividends are paid during the option's term, markets are efficient with no transaction costs or taxes, and continuous trading. 

These assumptions simplify the dynamics of markets to make the mathematical model workable.

Variables in the Black-Scholes Formula 

The model uses five key input variables: the current price of the underlying asset (S), which affects the option's intrinsic value; the strike price (K), determining the price at which the option can be exercised. 

Time to expiration (T), influencing time value and the likelihood of price movements; the risk-free interest rate ( r ), representing the cost of capital.

Volatility (σ), measuring the asset's price fluctuations - how much and how quickly the asset's price changes over time.

Understanding Volatility in the Model 

Volatility (σ) represents the degree to which the underlying asset's price fluctuates over time. 

In the Black-Scholes model, higher volatility increases the option's premium because it raises the probability that the asset's price will move significantly, potentially ending in-the-money. 

This is because greater uncertainty enhances the chance of favorable price changes for option holders. Volatility is a crucial input, as small changes can substantially affect the calculated option price.

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