The Excel Book Of The Dead: Bring Your Sheets Back To Life by Bisette Vincent & Van Der Post Hayden

Author:Bisette, Vincent & Van Der Post, Hayden
Language: eng
Format: epub
Publisher: Reactive Publishing
Published: 2024-01-09T00:00:00+00:00

Options Pricing Models and Greeks

Options pricing models serve as the cornerstone of financial derivatives trading. The most renowned of these is the Black-Scholes model, which revolutionized options trading with its analytical approach to valuing European options. Developed by Fischer Black, Myron Scholes, and Robert Merton, this model calculates the theoretical price of options by considering the stock price, strike price, time to expiration, risk-free rate, and volatility.

However, the Black-Scholes model does have limitations; it assumes a constant volatility and interest rate, and it cannot be used for American options, which can be exercised before expiration. For these reasons, extensions of the Black-Scholes model, such as the Binomial Options Pricing model, were developed. The Binomial model offers a flexible approach by breaking down the option's life into a series of discrete time intervals and calculating the price through a process resembling a lattice or tree.

To illustrate, let's consider a simple two-step binomial tree. Suppose a stock is currently priced at $100, and we want to calculate the value of a call option with a strike price of $105, expiring in one year. We assume that the stock can either go up by 10% or down by 10% in six months, with a risk-free rate of 5%. By computing the value at each node and discounting it back to the present using risk-neutral probabilities, we can estimate the option's value.

Now, let's shift our focus to the Greeks, which are named after Greek letters and provide a way to measure the sensitivity of an option's price to various factors. The most commonly used Greeks are Delta, Gamma, Theta, Vega, and Rho.

- Delta (Δ) measures the rate of change in the option's price with respect to changes in the underlying asset's price. For instance, a Delta of 0.5 implies that for every $1 increase in the stock price, the option's price is expected to rise by $0.5.

- Gamma (Γ) indicates the rate of change in Delta with respect to changes in the underlying price. This helps assess the stability of an option's Delta.

- Theta (Θ) represents the rate of change in the option's price as time to expiration decreases, often referred to as the time decay of the option.

- Vega (V) measures the sensitivity of the option's price to changes in the volatility of the underlying asset.

- Rho (ρ) gauges the sensitivity of the option's price to changes in the risk-free interest rate.

For those who craft their strategies based on these measures, let's consider an example with Delta. Assume we have a call option on a stock trading at $100 with a Delta of 0.6. If the stock price increases to $102, the option’s price would theoretically increase by $1.20 (0.6 x $2). Such knowledge is essential for constructing hedged positions in a portfolio.

By mastering options pricing models and the Greeks, financial professionals can not only value options but also gain a nuanced understanding of the risks associated with them. This knowledge is indispensable for creating sophisticated trading strategies that can adapt to changing market conditions.

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