Valuing Non-marketable Options

S

Spaghetti Code

My employer gives me the choice to put some of my salary into the company option plan. The options they grant are 10 year, ATM options, which cannot be bought or sold outside. The only way to exit the position is either to exercise, or sell back to the company for the intrinsic value. They vest immediately, and are non-qualified. There are no dividends announced or expected, and no splits.

Some questions on valuing these:

1. Is using Black Scholes reasonable on these? Since there is no way to sell the options back early and collect the time value, it would seem they are more European than American. In order to collect the full value, the options need to be held until expiration.

2. Assuming the above is a reasonable approximation, what does delta, gamma, vega, theta, or rho even mean? Since the value moves in lock step with the underlying, it would appear there is a discontinuity around the strike price. I tried modelling them with delta being 1 if above the strike, and 0 below, but what happens if it's exactly ATM?
 
Quick answer and it's gonna frustrate you. You ought to Google pricing long-dated options and you'll see BS doesn't work well. Volatility is also diminished in importance and net carry becomes more critical. Volatility curves are flatter. A good long-dated pricing model may be around if you can find anyone to sell one. Desks who do this kind of stuff don't - generally - give away the expected outcomes. Ask your treasurer how they value them. existing short-dated models will give you output data, but it isn't much good. Other folks on the site may have additional input.
 
7.10
LEAPS® Pricing
Options pricing models use five factors to determine an option's theoretical value:

  • Stock or ETF price
  • Strike price
  • Time to expiration
  • Interest rates (minus dividends)
  • Volatility of the underlying stock
For shorter-term options, it is common to use an interest rate that approximates the risk-free interest rate. Most people use the U.S. Treasury-bill rate (90-day).

Pricing longer-term options is more difficult than pricing shorter-term options. To price a LEAPS® option, it is necessary to predict volatility (expectation of price fluctuation) of the underlying stock and interest rates for up to 2-½ years. Of the factors mentioned, interest rates play a more significant role in the pricing of longer-dated options due to the length of time. As a result, even professionals struggle to quote prices for options with maturity dates far in the future. The predictability of the inputs is more unreliable than for shorter-term options. Changes in implied volatility can also significantly alter LEAPS® options’ premiums.

Despite difficulties, exchange policies generally require market makers and specialists to offer quotations (both bid and offer) for up to 10 contracts. This allows investors to find a market for LEAPS® at any time.
 
guru said:
https://www.investopedia.com/terms/e/eso.asp
"Your employer is required to specify a theoretical price of your ESOs in your options agreement. Be sure to request this information from your company, and also find out how the value of your ESOs has been determined."
More...

I didn't know they were required to provide this. That said, I would still prefer to do my own calculations (Trust but Verify). The company has mentioned that they typically lose money on the options they write (and thus I gain it), but again, going on their word. From my reading of their 10-Q, they use a binomial model with a suboptimal exercise factor around 3.
 
There are several white papers on valuing ESO’s. It was a hot topic in 2003 (for those who remember why and can grin slyly).

most companies use some form of black scholes and will explain the parameters in their annual report. However for you it’s really a form of funny money as you can’t trade it and it’s unlikely you will hedge it.
 
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