# Theta

### Meaning of Theta

Theta measures the change in Options price per day change in time to expiry. If theta is -3.87 that signify that for each day passes towards expiry the options price will decrease by 3.87.

### Important Points for Theta

- Theta of Option is always negative.
- Theta of Call and Put Option is same. (If rate of interest is not considered into calculation)
- Theta is highest at ATM and decreases as Underlying moves away.
- Theta of Future is 0.

When you buy Call Option, Negative Theta multiplies by Positive Quantity, hence gives Negative Portfolio Theta. This signifies that buying Call Option means Short Theta Position.

When you sell Call Option, Negative Theta multiplies by Negative Quantity, hence gives Positive Portfolio Theta. This signifies that Selling Call Option means Long Theta Position.

When you buy Put Option, Negative Theta multiplies by Positive Quantity, hence gives Negative Portfolio Theta. This signifies that buying Put Option means Short Theta Position.

When you sell Put Option, Negative Theta multiplies by Negative Quantity, hence gives Positive Portfolio Theta. This signifies that Selling Put Option means Long Theta Position.

Value of Theta increases as the Option moves from OTM - Out of the Money to ATM - At the Money and decreases as the Option moves from At the Money to In the Money Option.

### THETA Graph

### Theta with respect to change in SPOT PRICE:

**Observations: **As spot price increases

- Call premium increases and Put premium decreases.
- Call delta increases and Put delta decreases.
- Gamma is at peak at ATM and decreases as UNDERLYING moves away.
- Vega is at peak at ATM and decreases as UNDERLYING moves away.
- Theta is at peak at ATM and decreases as UNDERLYING moves away.

### THETA with respect to change in STRIKE PRICE:

**Observations: **As Strike price Increases

- Call premium Decreases and Put Premium Increases.
- Call Delta Decreases and Put Delta Increases.
- Gamma is at peak at ATM and decreases as UNDERLYING moves away.
- Vega is at peak at ATM and decreases as UNDERLYING moves away.
- Theta is at peak at ATM and decreases as UNDERLYING moves away.

### THETA with respect to change in DAYS TO EXPIRY:

**Observations: **As days to expiry decreases / time increases

- Both Call and Put Premium decrease.
- ATM Call Delta decrease and Put Delta increases (Both move towards 0.5).

ATM Gamma increases. - ATM Vega decreases. - ATM Theta increases.

### THETA with respect to change in VOLATILITY:

**Observations: **As Volatility increases

- Both Call and Put Premium increases.
- Call Delta increases and Put Delta decreases.
- ATM Gamma decreases
- ATM Vega decreases.
- ATM Theta increases.

### THETA with respect to change in RATE OF INTEREST:

**Observations : **As Rate of Interest increases

- Call Premium increases and Put Premium decreases.
- Call Delta increases and Put Delta decreases
- ATM Gamma decreases
- ATM Vega decreases.
- ATM Call Theta increases and Put Theta decreases.