Editing Financial derivatives (section)

== PUT-CALL options ==
We detail the design of two basic financial derivatives. PUT-CALL options and CALL-PUT options. The names indicate the partly symmetric function of these financial tools. The reason for the name is that inorder for one party to buy a put, a counterparty must buy a call. 

A PUT-CALL option on a DAO can be designed using a smart contract to limit the liability of the PUT buyer with the following design. Two parties encumber money in a PUT-CALL smart contract. The two parties are called the PUT buyer (whom we think of as the buyer of a traditional put option) and the CALL buyer. 

The PUT-CALL smart contract design is then given by the following basic flow:

# The CALL buyer encumbers <math>$P_0</math> cash<ref>Cash means the fungible unit of exchange on the platform which represents money, such as ETH in Ethereum or various stable coins.</ref> in the contract.
# The PUT buyer encumbers <math>$U>$P_0</math> cash in the contract. (Here <math>$(U-P_0)</math> represents the maximum amount the PUT buyer is willing to lose if the price of BONDs goes up instead of down. This is similar to the premium in a traditional put.)
# The PUT-CALL smart contract initates at time <math>t=0</math> and matures at time <math>t=T</math>.
# At maturity time <math>T</math>, the PUT-CALL smart contract checks to see if the PUT buyer has encumbered a BOND token in the contract.<ref>The rational PUT buyer purchases at market before time <math>T</math> if the price of BONDs <math>$P_T</math> is less than their encumbered <math>$U</math> cash. Since the PUT buyer has the opportunity to buy the BOND at any point before maturity, this contract is similar to a traditional [[wikipedia:Option_style#American_and_European_options|American option]].</ref>
#* If the price of a BOND has gone up beyond <math>$P_0</math>, the rational PUT buyer does not encumber the BOND at maturity time. So if the BOND is not encumbered, the contract gives $<math>U</math> to the CALL buyer and gives <math>$P_0</math> to the PUT buyer. (So the PUT buyer loses <math>$(U-P_0)</math>, which the CALL buyer wins.)
#* If the price of a BOND has gone down below <math>$P_0</math>, the rational PUT buyer buys a BOND at market for <math>$B_T</math> and encumbers the BOND before maturity time. Then the contract gives the BOND to the CALL buyer, and <math>$(U+P_0)</math> to the PUT buyer. (So the PUT buyer gains <math>$(P_0-B_T)</math>.)
A PUT-CALL option gives priority to the PUT buyer, as they can profit any amount up to <math>$P_0</math> if the BOND value collapses to $0, and the PUT buyer has limited liability of <math>$(U-P_0)</math> in case the BOND token's value explodes.  

<math>$P_0</math> may be thought of as representing the current market price of a BOND at initiation, though market prices are a fiction. So <math>$P_0</math> can be thought of as the strike price of the option for the PUT buyer. <math>$P_0</math> will typically be below the price <math>$B_0</math> that a BOND buyer can get at market when the contract initiates, in order for the PUT buyer to entice the CALL buyer to join the contract, because the value <math>$(U-P_0)</math> should be larger than what the CALL buyer thinks they can make <math>$(B_T-B_0)</math> from buying a BOND.

We can design the inverse scenario with a CALL-PUT option which focuses on the CALL buyer as follows.