# Gamma Weighted Average Price

Gamma Weighted Average Price (or "GWAP") is a pricing benchmark for block option order execution, similar to VWAP pricing used in the securities industry. Used in conjunction with VWAP pricing on the underlying stock or index, GWAP allows for execution of institutionally sized options orders at an understandable, fair price. This benchmark price is calculated based on trading activity over a period of time rather than on market conditions at a particular moment.

VWAP pricing adjusts the underlying benchmark price for different sized orders at different market prices over the pricing period. Similarly, GWAP pricing applies a calculation based on the option's gamma convexity to the order entry price to arrive at the benckmark option price. The resulting benchmark estimates the change in the option premium that would have resulted if the option had traded in volumes proportional to the underlying benchmark.

It should be noted that GWAP pricing does not weight the benchmark option price according to option volumes at various option prices througout the pricing period. This is impractical due to markets factors such as illiquid and inconsisent option trading activity and option spread trading.

## Products

GWAP will be used exclusively by CBOE, which in May 2008 signed a deal with 3D Markets, Inc., a block options trading firm that created the GWAP pricing.^{[1]}

## Formula

GWAP is calculated according to the following formula:^{[2]}

G_{wap} for a call option = Θ + [Δ^{2} * λ_{roc}]

G_{wap} for a put option = Θ - [Δ^{2} * λ_{roc}]

where

Θ = Order entry price set by the client with a corresponding delta, gamma, and underlying reference price.

Δ^{2} = γ * λ_{roc} + Δ^{1} (for calls); Δ^{2} = γ * λ_{roc} - Δ^{1} (for puts)

λ_{roc} = v_{wap} - Χ

v_{wap} = VWAP benchmark for underlying price

Χ = underlying reference price at order entry

Δ^{1} = Delta at order entry point

γ = Gamma at order entry point

## References

- ↑ www.3-dmarkets.com. 3D Markets, Inc.
- ↑ www.3-dmarkets.com/pdf/JOT-Winter-Edition-2008.pdf. The Journal of Trading, Winter 2008.