Option value

To value the call option , we can use the binomial tree or the put/call parity ecqution. Just curous , what is the difference?

Please add some comments. Thanks

binomail or bsm

put/call parity should give you the no arbitrage price of the option given the market assumptions. If the price of the call is this, and the underlying and strike price are this, the value of the put SHOULD be this.

The binomial tree is a model used to calculate the price of the option - put/call parity essentially gives you “what the price should be based on the strike price and underlying price of the asset today”

A binomial tree would be used by an investor, but is based on their own assumptions around volatility - for instance, if you think the volatility of the underlying will be X, how does that compare to what the market price of the option is or should be based on put/call parity?

Binomial Tree values an option based on the inputs: Upward % change, Downward % change, the risk neutral probabilities of moving up or down, risk free rate, sport price and strike price. This is a discrete time model. We can value of put or call using the tree and these inputs.

With Put/Call parity, we can value a put or call - but the inputs are different: we need 1) the present value of the strike price, 2) the spot price of the underlying and 3) either the call price or put price. Given 1) and 2) and the price of a call, we can value a put, or if we are given a put, we can value a call.

Put Call Parity allows us to value a Put or Call given the price of one or the other. Binomial Model actually calculates the price of an option with only raw inputs