- Fundamentally, there is no difference between puts and calls, and this insight itself is not dependent on a particular model or restricted to only particular parameter values. It is a deep truth.
The big intuitive insight from put-call parity is that it doesn't matter whether you trade in puts or in calls: the two are in some deep sense identical, despite their surface differences. Optionality is the key. The kink is the key. Once you have a kink, you can go long or short and you can fiddle with forwards to make it go up or down or left or right as you see fit.
The simplest proof:
C - P = long stock (from hockey stick diagram)
![notion image](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fec7cdada-ec0c-4cd4-a7ae-9c3654f73025%2FUntitled.png?table=block&id=cf2b625f-8508-4eaf-972a-4403fd0aecfc&cache=v2)
[image credit: TD Ameritrade]
Therefore:
C = long stock + put