Hi,I am trying to understand the difference between the economic values of two types of gift cards.1. Card 1 –the holder can buy merchandise worth $5 any time in the future.2. Card 2 – the holder can buy merchandise worth $5 can within next one month.It is obvious that card 2 has lesser economic value than card 1 due to its one-month time limit. Is there a way to quantify the difference between the values of the two cards?Also can I consider these gift cards as call options with a $0 strike price and $5 notional / face value? Thanks,MG.

No. The two cards have the same value. The maximal value it realizes is now, at $5, if interest/inflation rate is non-negative.What do you mean by notional and face value of an option? If notional/face value of an option is the current value of the option on the merchandise allowed to purchase, it is not a call option. You can consider this as a bond of notional $5 with an American option at $0 strike to redeem. But then again, the redemption time is now.

You got to know (model) the underlying price changes at the store, for a relative valuation (assume preferenses fixed and time insensitive), and presumably the consumer preferences for a complete valuation.Think toystore, and december for one gift card, then with a expected january sale. Then how much do you want toys, for the preferences bit. Perhaps toys on Christmas is worth a lot more for you? Then that would dominate and the gift cards would have equal value.

Interesting question.A call option gives you the right to buy a thing for a certain amount of money.If the gift certificate gave you the right to buy a certain toy for $5 then you could model it as a call option and the infinite duration option would be more valuable than the month option.The month duration option would probably be worth a couple of cents - all depending on how volatile toy prices are.But as knightrider says, you don't have a call option.But the tools of financial mathematics might not be the best place to start here. Maybe we should start by talking behavioural economics.Rationally a gift certificate makes no sense unless it is sold at a discount to the face value. It is a restriction of choice, product 2 being the most restrictive. But is it also a 'gift', which is a product with a value different from the purchasing power of it's $5 face value. The fact that there is a restriction on the store the $5 can be spent in actually adds value to the product. The store restriction is the gift, as it comes with a nice bit of thick paper normally with shiny writing on it and the words 'gift' printed somewhere.The month restriction is not part of this 'gift' premium. How should we value that. Maybe by looking at the second hand market for gift certificates on ebay? Or maybe by researching how gift certificates are spent. How many gift certificates are never redeemed? Does this change depending on the duration of the gift certificate? Basically is there a real market in second hand gift certificates, or in practice do people value the idea of the gift and disregard the monetary value?

Thanks a lot folks.I think I should have been more clear. Though I called them gift cards, they were not purchased for me by anybody. The store had a lucky draw. My friend got a price - a $5 gift card with no time restriction to spend that money. On the other hand, I also got a $5 card from the same store, but with a limited time restriction. Again I did not pay for my card. It is just a promotion item from the store. That got me thinking whether the economic value of these two cards the same.Quote knightrider said:What do you mean by notional and face value of an option? I was trying to say that with this option I can get things worth up to $5. I could not figure the right term for that variable. In finance options, generally, one call option allows the holder to buy one unit of the underlying asset. But in this case I was not sure what to call that $5 limit. MG.

Assuming a positive rate of inflation, you would redeem both gift cards today (or at least soon). Therefore, the time restriction should not be an issue. However, research has shown that many of these gift cards are never redeemed or are never fully redeemed. This is what makes it profitable for establishments to make use of gift cards. The same trend goes for rebates (even the ones that allow you to essentially buy the product for free). I am not aware of any research that disaggregates the likelihood of redemption by duration of the gift card. So, an interesting question would be what constraints prevent gift cardholders from redeeming these gift cards?

Let P(t) = probability of spending the gift card by time tValue of gift card with limited life-span n =$5 x P(n) + $0 x {1-P(n)} = $5 x P(n) Value of gift card with unlimited life =$5 x P(All n) = $5 x 1 = $5So the value difference will depend on your consumption preferences, which in turn determines P(t).

i disagree - first there is no option value to either card. this is because you can liquidate card and move into cash or sell the card to someone who is a motivated buyer of the goods offered by the card vendor. the only issue is what the discount should be for the inconvenience of having your shopping prescribed.

and if i may point out the behavioural aspect...an efficient market theorist would say "wow, this card is worth $5"while the store owner knows that once you enter the store, you are most likely going to spend a lot more than just 5 bucks...so what is the value of this gift card to the shopper, be it an option or not? it is negative.