Last resort... American Call Up & In... activities, accounting, management, corporate, internet

ishfaque

Hi guys,

I'm a level II candidate working in corporate finance for a large private company. I'm building a tool using Excel/VBA to integrate all the activities related to stock/option compensation to high management (accounting, taxes, HR, etc...).

Some of the options that they have are "American Up & In Call Option". I think I search the entire internet to find a model to value them, without success... I bought a book "Option Pricing Models & Volatility Using Excel-VBA", just received it today, they have model for every kind of options (American and European, Call and Put, Down and In, Down and Out, Up and In, Up and Out) except the "American Up & In Call Option" and the "American Down & In Put Option" (which logically must be related...).

So as a last resort, I'm testing the water here to see if anyone knows about a model to value those options... I guess worst case scenario I'll value them as European Up & In...

Thanks

segalm

Paul Wilmott Introduces Quantitative Finance includes a CD that has a sample barrier option model.

PalacioHill

use the closed-form formula for european up-and-in call. in theory, it should give you a lower bound. in further theory, once the call gets knocked in and becomes an ordinary american call, i dont see why you can't apply the same no arbitrage principle - i.e. american call on a non-dividend paying stock won't be exercised prior to maturity. so if the underlying doesn't pay dividends, then the closed-form european up-and-in price should be identical to the american up-and-in price.

in practice, the price is even lower (as opposed to higher) - you work for a private company (the underlying is illiquid), and this is executive comp (so the option itself is likely illiquid or with some transfer restrictions). there is no point in hunting down complex lattice models - the lack of liquidity in your case makes this exercise pointless. in summary, just use the closed-form european form.

tango_gs

Ok. Like jmh says, there is no analytical formula for this sort of option. You can solve for the value numerically using simulation or trees, but this would be a pain in the ass. If you're just looking for a value to put on your books, the European up and in model should be pretty close. Even if you had a better model, you would probably still have some error from volatility and drift curve assumptions.

LPoulin133

What if you just assume it's European and do it.
Isn't there some relation for normal American calls and puts that it is almost always better to sell it than exercise it early? If that applies to barriers, then you might save yourself some hassle.

And I don't recall binomial trees on any of the CFA exams...

SFoyil

Thanks guys for the responses.

@jmh530 : Yeah, I could build a binomial tree (all good stuff for level 2), and use the parity principle. But it seems it only applies to European options... For American Call Down-and-In and American Put Up-and-In we can use the reflection principle, which gives us a nice formula, but it doesn't apply to american Call Up-and-In.

@ohai: Exactly, the stock price is currently at 1$, the option is currently not activated, but as soon as it touch 3$, it becomes a normal american call option with a 1$ strike price.

I guess I would have to simulate the stock price evolution, and when it touches 3$, evaluate a normal american call option with the remaining maturity, or something like that.

KungFuPanda

That's what it means to me.

Colum

What is the exact contract definition of your "American Up and In Call Option"? Is this an American call option that knocks in if the underlier hits a barrier level?