Tuesday, October 13, 2009

Rho Rho Rho Your Boat

Put-Call Parity Concept helps to explain several phenomenon in the options world. Particularly in what seems to be a disparity in values of Calls and Puts of the same Strike and same expiration month.

For example, given the following scenario :

ABC Stock Price = $80
Interest Rate = 5%
Dividend Payout = $0.25

A 3-month Call - 80 Strike could be $3.75 and yet
A 3-month Put - 80 Strike could be valued at only $3.00

Question : Why is the Call more expensive than the Put, when they both have exactly the same probability of making or losing money?

The answer lies in none other than the Put-Call Parity Concept. Let me elaborate, by defining mathematically the Put-Call Parity. In essence, the formula can be gracefully expressed in the following manner :

Call + StrikeValue = Put + StockPrice + Interest - Dividend

==> Put = Call + StrikeValue - Interest + Dividend - StockPrce

Intuitively, when Interest component rises; such as the Fed Rates, then Call values INCREASE !! and at the same time, Put values DECREASE !!!

By now, it should be clear that if one is anticipating Fed Rates to increase, then, the market will start pricing Call options higher and everything else being equally, Put option values will drop.

And now, let's get back to the original question on why Calls are more expensive than Puts at the same Strike and same expiration month... It should be clear when we jiggle the Put-Call Party formula :

Stock = Call + StrikeValue - Put - Interest + Dividend

Using the above scenario, the formula easily translates to :

80 = 3.75 + 80 - 3 - 1 + 0.25

{Interest of $1 s calculated as 80 X 0.05 X [90/360] = 1}

If Call value was $3, just like the corresponding Put value, then the Stock price will be <$80, thus making this stock overvalued. This cannot be the case.

Incidentally, this Interest component that influence the values of options, is represented by the Greek - RHO

In summary, both Interest and Dividends components cause the disparity between Call and Put option values of the same Strike and expiration month....In the absence of dividends, then ultimately only the Interest component is responsible for the difference.