Based on the market price of the call option at a specific strike, a put option can be created by the following process: 1) buy the call at its market price, 2) sell the underlying stock at market price and 3) buy a bond at a discounted price that will equal the value of the strike price at the expiration date.
Arbitrage ensures that put prices will be related to calls at or near parity. For example, on Sept. 16, 2013, Citigroup stock is $51.00. One strike price is $45 with the corresponding call priced by the market at 7.05.
The current discount rate is one-half of 1% for one-third of a year to expiration, so the formula used to compute the put’s value is (-7.05 + 51 – 45 / (1.005)^0.333) x –1. The computed parity price, 0.9753, is close to the put’s market value of 0.9500.
The options market usually calculates the price of puts at or near the parity price with call options. “Citigroup January 2014” (below) is an excellent example of parity pricing. When calls are mispriced, the corresponding puts may be overvalued or undervalued at the same time. This pricing relationship supports the long straddle trades described above, with the possibility of originating a trade based on an undervalued call.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.