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extract from https://www.nber.org/papers/w5078.pdf

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?

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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.

  • I see. So basically, buying a mortgage from a borrower is implicitly modeled as writing 2 options. The call option is when there's a prepayment, the borrower "exercises" the buying of the mortgage back from the lender who looses the above market gains he could have had from higher interest rate the borrower is trying to avoid. The put option is also a risk as it results from default of payments, so the lender will only be paid back through the money from the price of the real estate he sells back which could be below the principal of the mortgage. – mabounassif May 10 at 15:10
  • The analogy is still not perfect in my mind for the put option. When the borrower defaults, the strike price of the option is changing which doesn't sound like the typical put option. – mabounassif May 10 at 15:14
  • @mabounassif It may be clearest to think about an interest-only mortgage where the principal balance is constant, say $200k. If the property value declines below $200k, the borrower can default and then the lender has effectively bought the property for $200k (the put strike). – nanoman May 10 at 19:35

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