Put-Call Parity

Put-Call Parity will allow us to price a put (or call) option given a call (or put), a bond and the stock. Conceptually, what the parity relationship is saying is that:

a protective put spread is equal to a call option plus bond position.

For a non-dividend paying stock, Put-Call Parity is:

\[C_0 + \frac{X}{(1 + r_f)^T} = S_0 + P_0\]

where:

• both the call and put options have the same strike price and expiration.
• the bond has an $X par value, which is the same as the strike price of the options.
• you can interpret the 0 subscript as 'today'.
• \(r_f\) is risk-free rate for bonds maturing at the same time as the options expire.

There are a couple important features of Put-Call Parity:

• Applies to European options only.
• Model and assumption free.

Let \(D\) be the expected dividend payment on the stock over the life of the option. Then the put-call parity relationship is:

\[C_0 + \frac{X}{(1 + r_f)^T} + \frac{D}{(1 + r_f)^T} = S_0 + P_0\]

Say we have the following values. How much is the put option premium?

stock = inputs[0][1]
rate = inputs[1][1]
strike = inputs[2][1]
call_price = inputs[3][1]
time = inputs[4][1]

put_price = call_price + strike / (1 + rate)**time - stock

print("Put price $", round(put_price, 1))

Put price $ 5.8