Editing Financial derivatives

[[BOND tokens|BOND token]] markets can be used in [[DAO Governance Framework|DGF]]  to create contracts with payout schemes which mimic the functionality of the legacy financial tools called [[wikipedia:Derivative_(finance)|derivatives]], i.e., various types of [[wikipedia:Call_option|call]] and [[wikipedia:Put_option|put]] options.

For instance a basic BOND already has some of the properties of a call option, since it serves as a claim on the future DAO earnings, through the REP salary. If the value of the DAO goes up, that typically means the REP salary goes up, which means the BOND increases in value. More complicated smart contract designs allow us to capture more of the properties of traditional call options. 

== PUT-CALL options ==
A limited PUT-CALL option on a DAO can be designed using a smart contract 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 PUT buyer encumbers <math>$U</math> cash in the contract. (This fixed amount $<math>U</math> is greater than the current market price <math>$P_0</math> of a BOND. So <math>$(U-P_0)</math> represents the maximum amount the PUT buyer is willing to lose if the price of BONDs goes up instead of down.)
# The CALL buyer encumbers the current market price <math>$P_0</math> of a BOND at initiation. 
# 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. (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.<ref>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 PUT buyer does not encumber the BOND at maturity time, then 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>$(U-P_0)</math>, which the CALL buyer wins.)
#* If the PUT buyer does encumber the BOND at maturity time, then the contract gives the BOND to the CALL buyer, and <math>$(U+P_0)</math> to the PUT buyer. (So the PUT buyer gains <math>$(P_0-P_T)</math> which the CALL buyer loses.)
# When the maturity of the PUT-CALL smart contract is reached at time <math>T</math>, the contract waits for the PUT buyer to encumber a BOND token in the contract (which the rational PUT buyer purchases at market if the price of BONDs <math>$P_T</math> is less than their encumbered <math>$U</math> cash).
#* If the PUT buyer does not encumber the BOND at maturity time, then 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>$(U-P_0)</math>, which the CALL buyer wins.)
#* If the PUT buyer does encumber the BOND at maturity time, then the contract gives the BOND to the CALL buyer, and <math>$(U+P_0)</math> to the PUT buyer. (So the PUT buyer gains <math>$(P_0-P_T)</math> which the CALL buyer loses.)

A PUT-CALL option gives priority to the PUT buyer. Similarly a CALL-PUT option gives priority to the CALL buyer as follows. 

== CALL-PUT options ==
In a CALL-PUT option, we again have two parties, called the CALL buyer and the PUT buyer. This time, however, the CALL buyer encumbers a BOND token instead of cash.

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

# The PUT buyer encumbers <math>$U</math> cash in the contract. (This fixed amount $<math>U</math> is greater than the current market price <math>$P_0</math> of a BOND. So <math>$(U-P_0)</math> represents the maximum amount the PUT buyer is willing to lose if the price of BONDs goes up instead of down.)
# The CALL buyer encumbers a BOND.
# The CALL-PUT smart contract initates at time <math>t=0</math> and matures at time <math>t=T</math>.
# At time <math>T</math>, the PUT-CALL smart contract checks to see if the PUT buyer has encumbered a BOND token in the contract. (The rational PUT buyer purchases at market before time <math>T</math> if the price of BONDs <math>$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]].)
#* If the PUT buyer does not encumber the BOND at maturity time, then 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>$(U-P_0)</math>, which the CALL buyer wins.)
#* If the PUT buyer does encumber the BOND at maturity time, then the contract gives the BOND to the CALL buyer, and <math>$(U+P_0)</math> to the PUT buyer. (So the PUT buyer gains <math>$(P_0-P_T)</math> which the CALL buyer loses.)