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Inputs for Black-Scholes Pricing of Options

Black Scholes Pricing ExplainedIn pricing stock options for some of our key employees, we are using a Black-Scholes calculator which asks for the following items: 1) Strike Price, 2) Share Price, 3) Maturity, 4) Risk Free Interest Rate, 5) Volatility. Our Board has confirmed the strike and share prices (based on internal revenue/profit targets) as well as the maturity but I unsure of %'s to use for interest and volatility. We are a privately held, growing company and would appreciate suggestions on what to use for #'s 4 & 5 above. Many thanks!

Answers

Carrie Roesner
Title: Controller and VP
Company: Centro
(Controller and VP, Centro) |

We're also a private company so hopefully I can help.

For the Risk Free interest rate, you'll want to look at your expected maturity, basically how long you think on average it will take people to exercise their options. Based on that estimate, you can use a US treasury bond rate for the closest maturity. For example, let's say you estimate the average time to exercise is 6 years, you can use the 5-year T-bond rate as your risk free rate.

For the volatility, we identified a peer group of public companies. From this group, you calculate the volatility of each company and you take a weighted average. We identified 4 companies and weighted them each equally but if one company is much more similar, you can weight it more heavily. For the actual calculation, we used a template - I'm sure your auditors can provide something for you to use.

Mark Lysynecky
Title: Controller (former)
Company: Investor Analytics
LinkedIn Profile
(Controller (former), Investor Analytics) |

Carrie - thanks so much for your suggestions. I will definitely go that route!

Andrea Bornschlegel
Title: Fractional CFO/Controller
Company: Financial Consultant
(Fractional CFO/Controller, Financial Consultant) |

You can also get peer group public company information from SEC filings (Edgar) rather than doing the calculations yourself -- i.e. pull up the latest 10K, search for the word Scholes to find their assumptions/values, then follow Carrie's weighting methodology.

Mark Lysynecky
Title: Controller (former)
Company: Investor Analytics
LinkedIn Profile
(Controller (former), Investor Analytics) |

Andrea - another great suggestion. Thanks!

Brad Luke
Title: SVP
Company: Software as a service
(SVP, Software as a service) |

This is a great thread, thank you. Andrea, great idea to search the SEC filings; volatility was always the most tricky assumption for me in the past. Yes, your auditors can provide you with a template for your calculations. Thanks.

Topic Expert
Jake Feldman
Title: Managing Director
Company: Global TaxFin Advisory Group LLC
(Managing Director, Global TaxFin Advisory Group LLC) |

I agree with the recommendations for how to estimate the parameters in a B-S model for valuing employee stock options. However, while the majority of companies do use the B-S model for this purpose because it's simple and fast, there is a large body of academic research that demonstrates the B-S approach can significantly overstate the value of employee stock options because it doesn't adequately handle the lack of marketability and vesting restrictions compared to more complex option models. Just do a web search "valuing employee stock options comparison of alternative models".

If such employee compensation is material, the company's earnings will be correspondingly depressed. Considering how finance people are often asked to put the best light on company performance, this is a legitimate area for enhancing earnings by using one of the alternative models.

Mark Lysynecky
Title: Controller (former)
Company: Investor Analytics
LinkedIn Profile
(Controller (former), Investor Analytics) |

Jake - thanks. This is something I will definitely have to explore further.

Mark Shornick
Title: CFO
Company: Numerix
(CFO, Numerix) |

Mark, you may find these links useful.
For risk-free rate, Treasury strips for the appropriate terms should suffice:
http://online.wsj.com/mdc/public/page/2_3020-tstrips.html?mod=topnav_2_3000.
For volatility, the prices in one of these indices may supply relevant data, though you'll need to calculate the vols for the appropriate terms with a standard deviation formula:
http://www.djindexes.com/investable-products/?assetclass=strategythematic.

Topic Expert
Jake Feldman
Title: Managing Director
Company: Global TaxFin Advisory Group LLC
(Managing Director, Global TaxFin Advisory Group LLC) |

Mark L, your very welcome. Since Mark S's Numerix is one of the leading [uhh, alright... the leading :)] derivatives pricing software firms, his PhD colleagues know more than all of us combined about option models.

Mark S, nice to hear from you again. You jogged another thought about how to estimate volatility. As you suggested, people often calculate volatility based on the standard deviation of historical returns; however, there is another commonly used approach that is thought to be better for estimating prospective volatility. That is to take a sample of existing comparable company options and use the B-S model to solve for the "implied volatility" using current option price quotes along with the estimates of the other model parameters. While it's no easy feat to do this algebraically, Excel Goal Seek makes it a snap.

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