Why do Pyramus and Thisbe kill themselves in Ovid's Metamorphoses?

Pyramus and Thisbe agree to meet in the woods and run away together after their fathers have forbade them to be together. Thisbe arrives first but is scared away by a lioness. When Pyramus arrives he sees the lion tracks and sees Thisbe's shawl, and kills himself thinking that Thisbe is dead. When Thisbe returns, she sees Pyramus' dead body and also kills herself.