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Options: Greeks and options' risks
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Options are volatile and risky instruments. The link between probability theory and investment risk makes it possible to quantify option investment risk in very precise ways. Any change in the variables used in the valuation model (interest rate, future price, days to expiration, and volatility) will affect the options' prices. These variables represent risks to an option portfolio. In the above section, we will define briefly most of the fundamental risks.

DELTA RISK.

The delta risk measures, for a certain underlying price, the impact on the option's price of a change in the underlying future price (generally quoted in cent for a change of 1 in the underlying price).

DELTA = (change in option price) / (positive change in asset price)

Example: Delta of 0.40 USD means that the option's price will increase by 0.40 USD if the underlying asset price increases by 1 USD. 

This risk indicator gives you an idea of the speed of reaction of the option.

A deep in the money option will usually have a delta close to +/- one, a far out of the money option will have a delta close to zero.

Perform a sensibility analysis with our Black and Scholes calculator

GAMMA RISK.

As the delta is not a constant and changes with the price of the underlying asset, the impact on the DELTA risk for each change in the underlying asset is called GAMMA risk. GAMMA can be positive as well as negative. The highest value is found close to the strike price.

A GAMMA of USD 0.05 means that the DELTA will increase by USD 0.05 for each dollar change in the underlying price.

Perform a sensibility analysis with our Black and Scholes calculator

LAMBDA RISK.

Very close to the GAMMA, the LAMBDA is defined as the percent change in the option price for a percent change in the underlying price.

LAMBDA is always greater (or close to) one.

THETA RISK.

The THETA risk measure the impact on the option's price of a one day change in time remaining to expiration

Perform a sensibility analysis with our Black and Scholes calculator

KAPPA / VEGA RISK

The option's price is affected by changes in the market's valuation of implied volatility. This very important risk is referred to as KAPPA or VEGA risk.

The KAPPA / VEGA risk is defined as Dollar change in option price for one positive point of implied volatility change 

Perform a sensibility analysis with our Black and Scholes calculator

RHO RISK

The last variable in the Black and Scholes model is the risk free interest rate. The impact on the option's price of a change in the risk free interest rate is referred to as RHO risk.

Perform a sensibility analysis with our Black and Scholes calculator

In the next topic, we will study the implied volatility.