I am trying to find how much the underlying price of a gold futures option must move in order to breakeven on owning an option for a day. I was hoping someone versed in pricing options could identify a flaw in my reasoning?
I am using an equation for calculating the profit and loss for a delta hedged option from. "option Trading Volatility: Trading Volatility, Correlation, Term Structure and Skew"Apr 24 2014 by Colin Bennett
P/L = 1/2 * GAMMA * S^2 - TIMEDECAY
S == the change in market price
Assume P/L = 0
S = SQRT(2*TIMEDECAY/GAMMA)
Here are some relevant variables I pulled from BLOOMBERG Option Valuation:
Option expiry = Feb 16th
Current Date = December 21st
ImpliedVol = 13.579%
Theta = -25.62 (sensitivity in option price to a decrease in 1 day of time to epxpiry)
Gamma = 9.342 (sensitivity of delta to a change in spot)
Price of GCH6 (Gold Future Underlying) = 1078.2 units
Contract Unit = 100 Troy Ounces
Price Quotation = U.S. Dollars and Cents per troy ounce
Minimum Price Fluctuation = .10$ per troy ounce
S = SQUAREROOT(2*THETA/GAMMA)
S = SQUAREROOT(2*25.62/9.342)
S = 2.34 = (2.34/1078.2)*100 = 0.21% , The market must move 0.21% during one day to breakeven
Unfortunately, this number is much smaller than the numbers I am getting using the MARS model on bloomberg, or than a number that would make sense given the history of the option. Each day I do the calculation its off by a factor of 3-5. I'm expecting a number in the 0.7% to 1.0% range.
Any ideas? I'm assuming the problem is units related, but I worry it could be equation related. Completely stumped.