# Monthly Archives: June 2012

## Put Call Parity

The term put call parity is an important concept for options traders to understand. What it means is that the price of a put option and the price of a call option are such that no risk free arbitrage opportunity exists to create profitable conversions or reversals. A conversion consists of a long put, long stock and a short call, while a reversal, or reverse conversion is the exact opposite, short stock, short put and a long call. The formula for put- call parity is as follows.

**C (t)-P (t) = S (t)- K x B (t, T)**

C (t) is the value of the call at time t

P (t) is the put value at time t

S (t) is the stock price

K is the strike price

B (t, T) is the value of a bond that matures at time T

The math is very simple and the concept is important for traders to understand. The reality of the market place is such that you won’t be able to find profitable conversions and reversals, because the arbitrage opportunities don’t exist, if they do they quickly disappear.

An alternative way to express it is;

**C -P = S – X + i – d**

Where;

C = The call premium

S = The Stock Price

i = Cost of Carry = X x R x T (years)

P = The Put Premium

X = The Exercise Price

d = The Present Value of Dividends

For traders looking at live market quotes it is simple to evaluate the three -sided relationship between the price of a call, a put and its underlying contract. Any one contract can be expressed in terms of the value of the other two, so;

Underlying Price = Call Price – Put Price + Exercise Price

Call Price = Underlying Price + Put Price – Exercise Price

Put Price = Call Price – Underlying Price + Exercise Price