System and method for determining a tradable value

A system configured to determine settlement values of derivative investment instruments representative of a state of market volatility, the system comprising:

• a communication interface configured for communication with at least external one data source remotely located from the system via a network;
• at least one data storage device storing data received via the communication interface, the received data corresponding to price and expiration information for a plurality of financial instruments predetermined as suitable as underlying assets for derivative investment instruments representative of the state of market volatility, wherein the plurality of financial instruments define one or more input sets, each input set comprising options contracts having a same underlying asset, different expiration dates and different expiration intervals;
• an order matching engine having a processor configured to receive a plurality of contra-position bids and offers and pair up the received contra-position bids and offers to complete trades between the paired received contra-position bids and offers;
• a settlement value processor in communication with the at least one data storage device and the order matching engine;
• and
• a program logic memory in communication with the settlement value processor and storing program instructions, the settlement value processor operative to execute the program instructions to:
• receive a plurality of input sets from the at least one data storage device or the order matching engine;
• select a portion of the plurality of input sets based on a plurality of selection criteria, wherein one of the plurality of selection criteria comprises option contracts having expiration dates less than 30 days from a current day;
• and
• generate a settlement value for the derivative investment instrument representative of the state of market volatility according to the settlement calculation relation:
• σ
• 2
• =
• 2
• T
• 
• ∑
• i
• 
• 
• Δ
• 
• 
• K
• i
• K
• i
• 2
• 
• 
• RT
• 
• Q
• 
• (
• K
• i
• )
• -
• 1
• T
• 
• [
• F
• K
• 0
• -
• 1
• ]
• 2
• where:
• T is a time to expiration;
• F is a forward index level;
• Ki is a strike price of ith out-of-the-money option—a call if Ki>F and a put if Ki<F;
• ΔKi is an interval between strike prices:
• ΔKi is the interval between strike prices—half the distance between the strike on either side of Ki:
• Δ
• 
• 
• K
• i
• =
• K
• i
• +
• 1
• -
• K
• i
• -
• 1
• 2
• further where ΔK for a lowest strike is a difference between the lowest strike and a next higher strike;
• likewise, ΔK for a highest strike is a difference between the highest strike and a next lower strike;
• K0 is a first strike below the forward index level, F;
• R is a risk-free interest rate to expiration;
• and
• Q(Ki) is a midpoint of a bid-ask spread for each option with strike Ki;
• and
• transmit a settlement value calculated according to the settlement calculation relation to a remote server.