put-call parity for binary options
Understanding Put-Phone call Parity
Put-call parity is an of import principle in options pricing kickoff identified by Hans Stoll in his paper, The Relation Betwixt Put and Call Prices, in 1969. It states that the premium of a phone call option implies a certain fair cost for the corresponding put option having the aforementioned strike price and expiration date, and vice versa. Support for this pricing human relationship is based upon the argument that arbitrage opportunities would materialize if in that location is a divergence betwixt the value of calls and puts. Arbitrageurs would come in to make profitable, riskless trades until the put-phone call parity is restored.
To begin understanding how the put-call parity is established, let's beginning take a look at two portfolios, A and B. Portfolio A consists of a european call option and greenbacks equal to the number of shares covered past the call option multiplied by the telephone call's striking price. Portfolio B consist of a european put pick and the underlying nugget. Note that equity options are used in this example.
Portfolio A = Call + Cash, where Cash = Call Strike Price
Portfolio B = Put + Underlying Asset
It can be observed from the diagrams above that the expiration values of the 2 portfolios are the same.
Phone call + Cash = Put + Underlying Asset
Eg. JUL 25 Call + $2500 = JUL 25 Put + 100 XYZ Stock
If the two portfolios have the same expiration value, then they must have the aforementioned present value. Otherwise, an arbitrage trader tin can go long on the undervalued portfolio and curt the overvalued portfolio to make a riskfree turn a profit on expiration day. Hence, taking into business relationship the need to summate the nowadays value of the cash component using a suitable gamble-free interest rate, we accept the following price equality:
Put-Call Parity and American Options
Since American style options allow early do, put-phone call parity volition not hold for American options unless they are held to expiration. Early practice will upshot in a deviation in the present values of the two portfolios.
Validating Option Pricing Models
The put-call parity provides a elementary examination of selection pricing models. Whatever pricing model that produces option prices which violate the put-call parity is considered flawed.
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Source: https://www.theoptionsguide.com/understanding-put-call-parity.aspx
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