TITLE:
Foreign Currency Mortgages Recast as Options on Commodity Futures
AUTHORS:
Rebecca Abraham, Joel Auerbach
KEYWORDS:
Aberrancy, Gamma, Wronskian Relations, Jump Diffusion, Currency Mortgage
JOURNAL NAME:
Theoretical Economics Letters,
Vol.9 No.7,
September
25,
2019
ABSTRACT: A foreign currency mortgage is debt for the purchase
of residential property denominated in foreign currency. The borrower makes
monthly payments in foreign currency. Devaluation of the domestic currency
results in higher monthly payments. Practitioners have proposed solutions to
avoid mortgage default. However, many of the practitioner solutions place excessive
financial burdens on foreign lenders, while relieving domestic borrowers of
responsibility. The goal of this paper is to present a solution that shares
responsibility equitably between borrowers and lenders. First, we evaluate
practitioner solutions by placing them in theoretical models. Then, the paper
presents a solution, in which mortgages (loans) are viewed as derivatives (not
loans). This is innovative, in that it takes mortgages out of banking and
places them within investments. We recognize that investors have differential
attitudes to risk. Accordingly, the proposed solution is presented in two
contexts, i.e. from the perspective
of a risk averse investor who shuns risk, or a risk taker, who is willing to
take excessive risk to pursue returns. In the proposed solution, a call buyer
may exercise the option, purchasing a futures contract to obtain the currency at
a strike price that is less than the spot exchange rate. During the lengthy,
uncertain delivery period, the exchange rate may vary more than the immediate
period defined by the spot rate, in the form of jump diffusion models with
stochastic volatility. The call buyer may purchase foreign currency at a strike
price equal to the forward rates of a series of 1-period futures contracts with
total life equal to the life of the mortgage. As strike prices continue to
increase, with domestic currency depreciation, a repayment vehicle in the form
of a portfolio of high-yielding securities is proposed, to produce the funds
needed to meet forthcoming increases in monthly payments.