To implement a volatility arbitrage strategy using option greeks, you can use the vega of the options to identify opportunities for arbitrage. Vega is a measure of an option's sensitivity to changes in the underlying asset's implied volatility. If the vega of one option is significantly higher or lower than the vega of another option with a similar expiration date, it may indicate an opportunity for arbitrage.
For example, if you are comparing the vega of a call option with a strike price of $50 to the vega of a call option with a strike price of $60, and the vega of the $50 strike option is significantly higher than the vega of the $60 strike option, it may indicate that the market is overpricing the $50 strike option relative to the $60 strike option. In this case, you could sell the $50 strike option and buy the $60 strike option to take advantage of the discrepancy in implied volatilities.
In addition to vega, you can also use the other option greeks to help manage risk and adjust your positions as the market conditions change. For example, you can use delta to hedge against changes in the underlying asset's price, and theta to adjust your positions as the options approach expiration.