If client and AP both have the Pairwise Master Key (PMK) available, why do we need a 4 way handshake again to derive some other key (PTK)? Why can't we use PMK for further security process?
The difference between the two keys is that the Master key (PMK) is supposed to be valid for at least as long as the client is connected. In the case of WPA-PSK, the PMK is the same from the moment the AP is configured until either the passphrase or the SSID changes. Therefore, if the PMK is compromised in any way, the attacker gains "permanent" access to the network.
To protect the PMK, the protocol derives a pair of Transient keys (PTK and GTK) that are used to directly encrypt communications. These may be expired and renegotiated several times in the course of the client's connection, and the compromise of either of them does not gain the attacker permanent access to the network. The next time the client connects, it will generate a new pair of Transient keys from random values generated on the AP and the client, combined with the PMK.