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Islamic Put-Call Parity
"Islam's prohibition on paying interest has made it difficult for many Muslims living in the West
to purchase homes. As a result, that prohibition has spurred some innovative home financing
techniques using put-call parity. In one of the simplest of these transactions, the bank buys
the house and sells it to its client for a higher price through an installment sale. Thus, instead
of owning the house and taking out a mortgage, which would be written as S(t) - K*e-r(T-t), the
client has agreed to buy the house, which can be written as C(t) - P(t). Viewed from the bank’
s perspective, it owns the house subject to the agreement to sell it to its client. Thus, the
bank’ s position can be written as S(t) + P(t) - C(t), which from put-call parity is equivalent to
K*e-r(T-t), a simple loan."