Valuing an American Option-Derivative Pricing in Excel

Follow us on LinkedIn

In the previous installment, we presented a concrete example of pricing a European option. In this follow-up post we are going to provide an example of valuing American options.

The key difference between American and European options relates to when the options can be exercised:

  • A European option may be exercised only at the expiration date of the option, i.e. at a single pre-defined point in time.
  • An American option on the other hand may be exercised at any time before the expiration date. Read more

An exact analytical solution exists for European options.  For American options, however, we have to use numerical methods such as Binomial Tree (i.e. Lattice) or approximations.  The post entitled How to Price a Convertible Bond provides an example of the Binomial Tree approach.

The Binomial Tree model is an accurate one. However, its main drawback is that it’s slow. Consequently, several researchers have developed approximate solutions that are faster. In this example we’re going to use the Barone-Andesi-Whaley approximation [1].

The Barone-Adesi and Whaley Model has the advantages of being fast, accurate and inexpensive to use. It is most accurate for options that will expire in less than one year.

The Black-Scholes Model is appropriate for European options, that is, options that may be exercised only on the expiration date. The Barone-Adesi and Whaley Model is designed for American options, which are options that may be exercised at any time before they expire. The Barone-Adesi and Whaley Model takes the value computed by the Black-Scholes Model and adds the value of the early exercise option that is available on American option.. Read more

Financial derivative pricing interest rate derivative

Government of Canada Benchmark Bond Yield. Source: Bank of Canada

Recall that the important inputs are:

Volatility

In this example we are going to use historical volatility. We retrieve the historical stock data from Yahoo finance.  We then proceed to calculate the daily returns and use them to determine the annual volatility. The resulting volatility is 43%. Detailed calculation is provided in the accompanying Excel workbook.

Stock price

The stock price is also obtained from Yahoo finance. It is 13.5 as of the valuation date (Aug 22 2018).

Dividend

The dividend yield is obtained from Yahoo finance. It is 1.2%. Note that for illustration purposes we use continuous instead of discrete dividend.

Interest rate

The risk-free interest rate is retrieved from Bank of Canada website. Since the tenor of the option is 3 years, we’re going to use the 3-year benchmark yield. It is 2.13% as at the valuation date.

We use the Excel calculator again and obtain a price of $3.32 for the American put option.

Derivative Pricing in Excel - Valuing an American Option

American option valuation in Excel

References

Barone-Adesi, G. and Whaley, R.E. (1987) Efficient Analytic Approximation of American Option Values The Journal  of Finance, 42, 301-320.

Further questions

What's your question? Ask it in the discussion forum

Have an answer to the questions below? Post it here or in the forum

LATEST NEWSU.S. Crude-Oil Inventories Fall More Than Expected
U.S. Crude-Oil Inventories Fall More Than Expected

Crude-oil stockpiles fell by 4.6 million barrels last week, more than analysts’ forecasts for a 1 million-barrel decline, government data showed. Gasoline stockpiles increased by a greater-than-expected 5.4 million barrels.

Stay up-to-date with the latest news - click here
LATEST NEWSSwitzerland Charges Trafigura and a Former Top Executive With Bribery
Switzerland Charges Trafigura and a Former Top Executive With Bribery

A former chief operating officer is accused of helping to funnel millions of dollars to an Angolan official, including cash payments.

Stay up-to-date with the latest news - click here
LATEST NEWSMcDonald’s Targets 50,000 Restaurants in Expansion Blitz
McDonald’s Targets 50,000 Restaurants in Expansion Blitz

McDonald’s Corp. is looking to hit 50,000 locations around the world by 2027 in what the company calls the fastest expansion spurt in its history.

Stay up-to-date with the latest news - click here
LATEST NEWSFacebook parent sued by New Mexico alleging it has failed to shield children from predators
Facebook parent sued by New Mexico alleging it has failed to shield children from predators

Santa Fe, N.M. (AP) — Facebook and Instagram fail to protect underage users from exposure to child sexual abuse material and let adults solicit pornographic imagery from them, New Mexico’s attorney general alleges in a lawsuit that follows an undercover online investigation. “Our investigation into…

Stay up-to-date with the latest news - click here
LATEST NEWSUS attorney general defends prosecutions of Jan. 6 rioters
US attorney general defends prosecutions of Jan. 6 rioters
Stay up-to-date with the latest news - click here

Leave a Reply