It is more like a call option. This is because by making the down payment (premium), the purchase price of the house (strike price) is locked in. Even if the house price increases in the future, you can purchase the house at $250,000 by making the loan payments. However, the house can only be owned after 30 years (expiration date) when the loan payments are completed.
Therefore, in this case :
strike price = cost of house = $250,000
premium = down payment = $250,000 * 20% = $50,000
expiration date = date of completion of mortgage payments = 30 years from today
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