Modeling a Down Payment as a Call Option

There was an interesting idea that came up in our discussion of Islamic Finance that got me thinking. While not directly related to what we were doing, someone mentioned the idea that a down payment was modeled like a call option which I thought was quite clever.

Consider this, you can:

• put down a payment for the right to purchase the asset
• elect to walk away from this right, forfeiting the down payment, or
• pay the *remaining amount* and purchase the asset at the appropriate time

This is very similar to a call option, with only one exception:

Note that in a down payment, you are paying the remaining amount, not the full amount of the asset. So if you were to use a call option to model down payment, you would have to adjust the strike price down by the premium (down payment) because the down payment is applied to the purchase price of the asset.

So imagine that the value of your asset changes after you’ve paid the down payment. If it goes up, you can continue your purchase (and possibly even sell your asset for a profit, assuming its liquid enough) or you can elect not to buy it if you’ve taken a huge bath (maybe even the market value dropped by more than the down payment amount).