Can someone explain to me how does it benefit the mortgage holder to be a writer of the option call on the long term debt and the put option on real estate prices? Other than the premium be gained I don't see how the benefits outweighs the risk, and why would anyone actually exercise the option of buying a long-term debt with a high interest rate that is about to be refinanced?
The short put on real estate represents an increased risk, for which mortgage pricing effectively includes a premium. But because the mortgage holder (lender) has already bought a long-term debt instrument, the short call on debt is a covered call. It caps the gains if rates fall, but doesn't introduce large downside. The comparison is to an ordinary (non-refinanceable) bond plus a short call. In this analogy, the exercising call owner would be buying a bond that has risen above a strike price. That is effectively the same benefit that the borrower gets by refinancing.