In one of my previous posts, I mentioned something about the mathematics of futures contracts and asked if anyone would like for me to expound upon the reference I made, and my co-author Samantha Goldflake (as well as other readers) called me out on it, so here goes.
First, I'd like to introduce what a financial derivative is, and from that what a futures contract is and how to value it. A financial derivative has nothing to do with the slope of a tangent line, but rather is an asset which derives its value from some underlying asset. Examples of this include mutual funds, put and call options, interest rate swaps, and futures. These assets all have no value whatsoever on their own, but only derive their value from what some other asset is doing. Many of the stocks in SL are actually financial derivatives.
As a personal note, I love financial derivatives. Financial derivatives are power. I've been asked, and have provided, guides and advice as to how to implement financial derivatives in Second Life to various exchange bigwigs, but so far nothing has come above of it. If any of you are considering doing something with derivatives, please send me an IM - I'd love to be involved.
To me, the most viable financial derivative for Second Life would be a futures contract. A futures contract specifies that an investor will either buy or deliver a set amount of an underlying asset at a set price at a set time. There is no option as to whether or not this sale/purchase will take place - it is set by the contract.
A lot of the numbers you hear tossed about in First Life financial commodities are actually futures numbers. The price of oil, for example, is almost always quoted as a futures price. The same is true with gold, silver, and other precious metals.
So how could you use this in Second Life? Simple - futures on the LindeX. Set up a price and a date, and then you've got a futures contract with USD for L$. Measures would have to be taken to prevent simply bailing out on the contract, but having investors place and x% deposit for taking the contract would probably suffice, depending on what x is.
Regardless, we may wish to know how to price these funky things called futures. It's actually surprisingly simple, and most of the mathematics I've already covered in my first Lessons in FM: Part I - Present Value. Technically, futures contracts with strike prices (the price specified in the contract) equal to the expected cost have zero premium, although in real trading there is always some transaction cost to doing this.
I slipped in the word "expected" to the definition above for a reason. Suppose we're doing a futures contract on a five-year zero-coupon bond yielding 10% per year, costing 1000 now and with an expiration date of 6 months from now. If the strike price is 1000, that contract will actually trade at a premium because 6 months from now the bond is worth more than 1000. We would expect it to be worth
1000*(1.10)1/2 = 1048.81
So the contract actually has a value of 48.81. For the contract to have zero premium, it must have a strike at the expected price of 1048.81, and then it will have zero premium.
First, I'd like to introduce what a financial derivative is, and from that what a futures contract is and how to value it. A financial derivative has nothing to do with the slope of a tangent line, but rather is an asset which derives its value from some underlying asset. Examples of this include mutual funds, put and call options, interest rate swaps, and futures. These assets all have no value whatsoever on their own, but only derive their value from what some other asset is doing. Many of the stocks in SL are actually financial derivatives.
As a personal note, I love financial derivatives. Financial derivatives are power. I've been asked, and have provided, guides and advice as to how to implement financial derivatives in Second Life to various exchange bigwigs, but so far nothing has come above of it. If any of you are considering doing something with derivatives, please send me an IM - I'd love to be involved.
To me, the most viable financial derivative for Second Life would be a futures contract. A futures contract specifies that an investor will either buy or deliver a set amount of an underlying asset at a set price at a set time. There is no option as to whether or not this sale/purchase will take place - it is set by the contract.
A lot of the numbers you hear tossed about in First Life financial commodities are actually futures numbers. The price of oil, for example, is almost always quoted as a futures price. The same is true with gold, silver, and other precious metals.
So how could you use this in Second Life? Simple - futures on the LindeX. Set up a price and a date, and then you've got a futures contract with USD for L$. Measures would have to be taken to prevent simply bailing out on the contract, but having investors place and x% deposit for taking the contract would probably suffice, depending on what x is.
Regardless, we may wish to know how to price these funky things called futures. It's actually surprisingly simple, and most of the mathematics I've already covered in my first Lessons in FM: Part I - Present Value. Technically, futures contracts with strike prices (the price specified in the contract) equal to the expected cost have zero premium, although in real trading there is always some transaction cost to doing this.
I slipped in the word "expected" to the definition above for a reason. Suppose we're doing a futures contract on a five-year zero-coupon bond yielding 10% per year, costing 1000 now and with an expiration date of 6 months from now. If the strike price is 1000, that contract will actually trade at a premium because 6 months from now the bond is worth more than 1000. We would expect it to be worth
So the contract actually has a value of 48.81. For the contract to have zero premium, it must have a strike at the expected price of 1048.81, and then it will have zero premium.
To value these contracts then, you have to figure out your payoff and then discount it back to the present value. That's where my previous post comes into play - present value. The payoff on a forward contract is simply:
With the profit equal to
Therefore, to calculate the value for a futures contract expiring at time t, just calculate
Where i is the interest rate being used. i varies depending on what you're valuing. With bonds, it's the interest rate. With stocks, it tends to be the dividend yield. With currencies, it's the interest rate in the currency you're using. So, for my futures contract on the LindeX, we'd have to use the Second Life interest rate (or USD interest rate, if we were buying the Lindens) to discount to present value.
I hope this helps demonstrate what futures are and how they work. As I mentioned above, they're used quite frequently in real-life commodity trading, and almost every farmer in the United States is familiar with them. (They tend to sell futures contracts early in the season to ensure they sell their crop at harvest.) If you have any questions, by all means ask!
GM
1 comments:
Thanks a lot! I'll be pasting your lessons on a document, so I can have them handy anywhere, anytime :)
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