# Using Financial Instruments to Transfer the Information Security Risks
## 6 Design Specifications for Information Security Derivatives
### Risk Mitigation with ISD  
The ISD contracts are the financial instruments that derive their values from the probability of occurrence or non-occurrence of the underlying event. Therefore, their value depends on the future events. They are a form of contractual agreement between the buyer and the seller to exchange the privileges and liabilities linked to the underlying event. There are at least two parties involved in the trading of ISD. Therefore, the accounting gains made by one party are exactly equal to the accounting losses suffered by the counterparty. This is similar to the cash settled traditional derivatives. Let us consider an ISD contract that has two \"states\", State-1 and State-2 denoted as \"\(s_{1}\)\" and \"\(s_{2}\)\" respectively. The total investment in the state \(s_{1}\) is \"\(T_{s_{1}}\)\" and in the state \(s_{2}\) is \"\(T_{s_{2}}\)\". If the state \(s_{1}\) occurs then the unit payout for the same is, \"\(U_{s_{1}}\)\" as expressed in Equation (1). \[U_{s_{1}}=\frac{T_{s_{2}}}{T_{s_{1}}} \tag{1}\]  
Similarly, if the state \(s_{2}\) occurs then the unit payout for the same is, \"\(U_{s_{2}}\)\", as expressed in Equation (2). \[U_{s_{2}}=\frac{T_{s_{1}}}{T_{s_{2}}} \tag{2}\]  
The unit payout for the occurrence of an event with more than two states can be calculated as expressed in Equation (3). \[U_{s_{i}}=\frac{\sum_{j=1}^{n}T_{s_{j}}}{T_{s_{i}}} \tag{3}\]  
\[\text{where}\quad j\
eq i\]  
In the Equation (3), the state \(s_{i}\) is the state for which the unit payout \"\(U_{s_{i}}\)\" is calculated. \"\(n\)\" is any positive number indicating the highest number of possible states (outcomes) for the given event. The total investment in any given state is represented as \"\(T_{s_{i}}\)\". \"\(T_{s_{j}}\)\" is the total investment in all the states other than the state \"\(i\)\". In the above scenario of an event with two states, if a trader invests an amount of \"\(I_{s_{1}}\)\" in state \(s_{1}\) and if the said state occurs, then the total payout received by the trader is, \"\(P_{s_{1}}\)\", as expressed in Equation (4). \[P_{s_{1}}=I_{s_{1}}*(\frac{T_{s_{2}}}{T_{s_{1}}+I_{s_{1}}}+1) \tag{4}\]  
If the state 2 \"\(s_{2}\)\" occurs then the payout is, \"\(P_{s_{2}}\)\", as expressed in Equation (5). \[P_{s_{2}}=0 \tag{5}\]  
If the trader wants to hedge his risk exposure to the occurrence of state \"\(s_{2}\)\", then the investment required for \"\(s_{2}\)\" can be calculated by equating the payouts in both the states with the planned hedge trade, as expressed in Equation (6). \[P_{s_{1}}=I_{s_{1}}*\left(\frac{T_{s_{2}}+I_{s_{2}}}{T_{s_{1}}+I_{s_{1}}}+1 \right)=P_{s_{2}}=I_{s_{2}}*\left(\frac{T_{s_{1}}+I_{s_{1}}}{T_{s_{2}}+I_{s_{2 }}}+1\right) \tag{6}\]Solving the above equation gives the investment which the trader is required to do in state \"\(s_{2}\)\", as expressed in Equation (7). \[I_{s_{2}}=\frac{I_{s_{1}}*T_{s_{2}}}{T_{s_{1}}} \tag{7}\]  
As shown in above equations, compared to traditional derivative instruments, the calculation and implementation of hedge trades using ISD is relatively straight forward. The hedge ratio \(I_{s_{2}}\) computed for a simple two state instrument can be extended for the instruments with more than two states. Further, as the set of states in ISD consist of all the possible and mutually exclusive states, the states that can occur other than in which an investment has been made by a trader can be termed as \"complementary states\". The process of hedging for a multi-state event consists of two steps, as follows:  
* Determine the hedge amount to be invested in the complementary states
* Distribution of the said amount among the complementary states  
The first step, determining the amount of investment required in complementary states is calculated as in Equation (8).