Tuesday, July 9, 2013

Ockhams Formula (Option Valuations)

Ockham's Razor has often been interpreted as "when you have two competing theories that make exactly the same predictions, the simpler one is the better." In the case of option valuations, I have found Ockham's Formula (Gallacher) significantly more practical than Black Scholes for a couple of reasons:

1) Ockham's is much simpler to apply and offers very similar accuracy as BS for ATM (At The Money) options.

* While Ockham's is not explicitly able to estimate fair value of OTM (Out of The Money) options, BS estimates are wildly inaccurate.

2) Ockham's gives answers where BS fails for options near expiration.

Ockham's ATM Option valuation

ATMO = S * 0.5 *  MAD * SD
             = S * 0.5 * sqrt(2/pi) * SD
             = S * 0.4 * SD
             = S * 0.4 * V * sqrt(T/254)
             = S * V / 40

ATMO = ATM fair value option price
S = Underlying product value
V = Realized volatility
T = days until option expiration       

Ockham's Option decay estimate
It is similar to theta, except this is much more accurate near expiration.

D(t, T) = 100 * [1 - sqrt(t/T)]

D(t, T) = Decay as a % of option price up to time t
T = days until option expiration   
t = days from expiration

For example, between the 4th and 5th trading days until expiration, an option is expected to lose
100 * [1 - sqrt(4/5)] = 10.5573%