#early exercise

The early bird catches the worm.

🐦🐛⛅

Did a little 40min fitness blender workout because I must be crazy! Then took the dog for his nice walk. Now it's my weekly trip to the shops and then home for baking banana bread, maple and pecan Danish and homemade protein bars.

Today I woke up an hour earlier (at 7am) so I could have my wake up coffee time & be out the house before it got to unbearable hot. I left at 8:47am It was still 23degres. I did also remember to wear a hat! And I went a slightly different run route just cause I needed to mix it up a bit.

If you're interested in pricing derivatives with early exercise using Monte-Carlo, you may have heard of the Longstaff-Schwartz method.

When pricing a derivative using Monte-Carlo, you generate a large number of potential price paths of the underlying, and determine the value of the derivative payoff on each path. The fair price of the derivative is then simply the average across all of the potential paths. When the derivative is callable / has an early exercise feature, an additional complexity is that to value the derivative on each path you need to work out at which time step the holder would exercise the derivative. This is the first time step at which the payoff from exercising is higher than the expected payoff from continuing.

Longstaff and Schwartz devised a clever method for determining the expected value of continuing. It involves fitting a straight line to a scatterplot, and then applying an optimization routine to adjust the line into the position that exercises/continues optimally.

I wondered, what if instead of a straight line we used a more complex non-parametric curve? Could we get better results?

What I found was interesting. The straight line approach is sufficient as long as the function representing the value of exercising and the function representing the value of continuing do not intersect at more than two points. For a derivative with a complex payoff with more than two intersection points, the straight line method would fail and a non-parametric curve fitting would succeed.

I also found that the essence of the Longstaff-Schwartz method is not really curve fitting, but something more akin to machine learning, and classification methods like a support vector machine.

Most start up employees don't realize that it's possible to by pass the 1 year cliff period after receiving the options grant.If you exercise your options before they vest i.e. early exercise, you’ll receive Restricted Stock but not Common Stock. If you quit, the company can purchase/buy back the Restricted Stock purchased at the amount you paid . Restricted stock vests into Common Stock at the same schedule as your options would vest. So if you did an early exercise/forward exercise, on the 1st year anniversary 25%of the Restricted Stock (assuming1 year cliff and 4 year vesting schedule) vests and become Common Stock without the need of any paper work . If that happens, the company cannot force you to sell them even if you quit.

About The Author

Arushi Bhandari, CPA, MBA recently published an eBook “STARTUP Financing, Equity and Tax" with insights about the impact of JOBS Act & Dodd Frank Act on startup funding, terms like angel, accredited investors, venture capitalists, stock options, Restricted Stock, RSUs. It gives in depth examples & templates explaining documents like Term Sheet, Cap Table, Convertible Securities plus the importance of 83(b) filing.

Links to Download Arushi’s eBook Apple iBook: STARTUP Financing, Equity and Tax Kindle edition STARTUP Financing, Equity and Tax