• Options Greek Functions

    Delta

    It denotes the rate of change of option price with respect to the price of the underlying asset. Call option premium increases with the increase of the underlying asset price as it increases the intrinsic value (for in-the-money option) or brings the underlying asset market price closer to the strike price (for out-of-the-money option). Put option premium decreases with the increase of the underlying asset price as it decreases the intrinsic value (for in-the-money option) or pushes the underlying asset market price more far to the strike price (for out-of-the-money option). So Call option premium is positively co-related to Delta while Put option premium is negatively co-related to Delta.

    Theta

    Theta of a portfolio of options denotes the rate of change of the value of the portfolio with respect to the passage of time with all else remaining the same. The time value of an option decreases with the decrease of duration until the expiry date or more the expiry date come closure. Because of this call and put option premiums are positively co-related with the theta as both of them decrease with the decreased time to maturity.

    Vega

    The Vega of a portfolio of derivatives denotes the rate of change in the value of the portfolio with respect to volatility of the underlying asset. As the volatility increases both the call and put option premium, both of them are positively co-related to the Vega.

    Rho

    The Rho of a portfolio of options denotes the rate of change of the value of the portfolio with respect to the interest rate or the risk free rate. From the Put call parity or option valuation technique we can see that the increase in risk free rate increases the call option premium and decreases the put option premium. So call option premium is positively co-related to Rho while Put option premium is negatively co-related to Rho.

    In Tabular form,

    Sensitivity Factor Input Calls Puts
    Delta Asset Price Positively Related Negatively Related
    Vega Volatility Positively Related Positively Related
    Rho Risk Free Rate Positively Related Negatively Related
    Theta Time to expiration Value -> 0 as call -> maturity Value -> 0 as Put -> maturity

    Gamma

    It denotes the rate of change of the option’s Delta with respect to the price of the underlying asset. Gamma is maximum when the underlying asset or security price is near to the strike price and it decrease with the increased difference between the underlying security or asset price and strike price.

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