Bjerksund Stensland Model: A Comprehensive Guide to Option Pricing

The Bjerksund Stensland Model is a popular method for pricing options, and it's widely used in finance. It's a relatively simple model that's easy to understand and implement.

This model was developed by Øyvind Bjerksund and Ingrid Stensland in 1993. They were Norwegian academics who created this model to provide a more accurate estimate of option prices.

The Bjerksund Stensland Model takes into account the underlying asset's volatility, time to expiration, and interest rates. It's a binomial model that assumes the underlying asset's price can only move up or down at each time step.

By using this model, investors can get a better sense of the potential risks and rewards associated with buying or selling options.

The Bjerksund-Stensland model is a closed-form option pricing model used to calculate the price of an American option. It was developed by Norwegians Petter Bjerksund and Gunnar Stensland in 1993.

The model is specifically designed to determine the American call value at early exercise when the price of the underlying asset reaches a flat boundary. It works for American options that have a continuous dividend, constant dividend yield, and discrete dividends.

The Bjerksund-Stensland model takes into account that options may be exercised before the expiration date, unlike the Black-Scholes model. This means the latter isn't really suitable for calculating the price of American options and works best when pricing more straightforward European options.

The model factors in that U.S. options may be exercised before the expiration date. It also considers the effect of dividends on the option's value, as dividends reduce the stock price and can impact the optimal exercise decision.

To calculate option prices using the Bjerksund-Stensland model, you need to input several parameters, including the stock price, strike price, time to maturity, risk-free interest rate, dividend yield, and volatility.

Here are the key parameters you need to input:

The Bjerksund-Stensland model is more accurate than the Black-Scholes model for American-style options, but it still has its limitations. It assumes constant volatility, no transaction costs, and a continuous dividend yield, which may not always be the case in real-world scenarios.

The Bjerksund-Stensland model is a powerful tool for financial analysts and traders alike. It's particularly useful for American-style options, where it can handle early exercise decisions.

One of the key strengths of the Bjerksund-Stensland model is its ability to incorporate the cost of early exercise, which sets it apart from other option pricing models like the Black-Scholes model. This model assumes options will only be exercised at expiration.

The Bjerksund-Stensland model also takes into account the impact of dividends on option pricing, which can have a significant effect on the value of options, especially for stocks that regularly distribute dividends. By incorporating the dividend yield and timing into the model, analysts can accurately estimate the impact of dividends on option prices.

To implement the Bjerksund-Stensland model, it's essential to ensure that the necessary inputs are accurate and up-to-date. This includes variables such as the stock price, strike price, risk-free interest rate, volatility, dividend yield, and time to expiration.

The Bjerksund-Stensland model offers a comprehensive approach to option pricing that considers early exercise decisions and dividend impacts. By leveraging this model, financial analysts and traders can accurately value options and make informed investment decisions.

In a case study, an investor holding an American-style call option on a stock with a strike price of $50, a current stock price of $55, a risk-free interest rate of 5%, and a time to expiration of 6 months can use the Bjerksund-Stensland model to determine the fair value of the option.

The model requires inputting the current stock price, strike price, risk-free interest rate, time to expiration, dividend yield, and the cost of carry to calculate the option price. In this case, the dividend yield is 2% and the cost of carry is zero.

By plugging in the values into the Bjerksund-Stensland model, the investor can calculate the fair value of the American call option. The model can also perform sensitivity analysis to observe how changes in variables affect the option price.

The Bjerksund-Stensland model is just one of many option pricing models available, and it's always beneficial to compare the results obtained from different models to gain a comprehensive understanding of the option's fair value.

The Bjerksund-Stensland Model has several advantages that make it a useful tool in finance. One of its key benefits is that it can complete complex calculations more quickly and efficiently than many other pricing methods.

Its ability to enable the early exercise of options contracts is also a significant advantage. This can be especially useful for public companies that need to determine whether dividends can be declared based on existing financial conditions.

The model's principle can also be applied to implied volatility, spreads, and asset movement forecasting studies, making it a versatile tool in finance. However, the model is not without its limitations.

One of its main limitations is that it cannot be applied to options other than American options. This means that it has a limited scope of use compared to other pricing models.

Here are some specific advantages and limitations of the Bjerksund-Stensland Model:

To implement the Bjerksund-Stensland model in Excel, you need to set up the necessary inputs, including the current stock price, strike price, risk-free interest rate, time to expiration, volatility, and dividend yield.

These inputs can be easily updated and modified by inputting them into designated cells in Excel. You can also utilize named ranges for inputs to improve clarity and ease of use.

To calculate the option price, you can use the built-in Excel functions, such as the NORM.S.DIST and NORM.INV functions, to calculate the cumulative standard normal distribution and inverse cumulative standard normal distribution, respectively.

Double-checking formulas and inputs for accuracy is crucial to avoid potential errors, so make sure to review your work carefully.

Excel's flexibility allows for easy sensitivity analysis and case studies using the Bjerksund-Stensland model, enabling you to assess the impact of various factors on option pricing.

By changing the inputs, such as volatility or dividend yield, you can observe how the option price reacts to different scenarios, providing valuable insights for risk management and decision-making purposes.