ZTE Quant Research

This page has two sections:

• The Calculator
• Greek Sensitivities Visualization Tool - the Greeks Diagram

The Calculator

The handy and versatile calculator presented on this page allows users to quickly calculate an option's theoretical value, and/or deduce an option's implied volatility if option's market price is given. Option's risks metrics - Greek Letters - are also provided.

Parameters on Input Panel

• Model

Currently we support three valuation models: Black-Sholes, Monte Carlo and Binomial.

Monte Carlo Model: Number of Paths = 20,000; Number of Time Steps = 100

Binomial Model: Number of Time Steps = 500

• Option Type

Both European and American style options are supported.

•  Stock Price

The Price of the underlying stock.

•  Strike

The exercise price defined in the Call or Put option. It is the price that the stock can be purchased (for call) or sold (for put) obliged by the contract.

•  Volatility

The annualized volatility (standard deviation) of the underlying stock price return, in percentage terms. For example, 20% volatility means one standard deviation of the annual price change for the underlying stock is 20%.

•  Time to Maturity

How long before option expires. Enter the length of time in terms of days or years.

•  Dividend Yield

The expected annual dividends from the underlying stock divided by stock spot price, in percentage terms.

•  Risk-Free Rate

Risk-Free interest rate in percentage terms.

 

Parameters on Theoretical Value and Greeks Panel

• Theo Value

The theoretical value of the option based on chosen financial model and valuation parameters. Note this may or may not be the same as market value, which is also affected by demand and supply.

•  Delta

The rate of change in option price with respect to the change of underlying stock price. Note delta is not constant and only measures very small change in underlying stock price.

•  Gamma

The rate of change in option's delta with respect to the change of underlying stock price. Gamma measures the curvature of the delta.

•  Vega

The rate of change in option price with respect to the change of 1 percentage point change in volatility of the underlying stock.

•  Theta

The change of option price with the passage of one day when other things remain constant.

•  Rho

The change of option price with respect to one percentage point change in risk-free interest rate.

 

Parameters on Implied Volatility Panel

• Option Premium

The observed market price of the option for calculating implied volatility.

•  Implied Volatility

The volatility of the underlying stock price, implied by the option market price based on valuation model.

 

Greeks Diagram

A more powerful tool - Greek's sensitivities vs. market variables are fully visualized in the Greeks Diagram:

• The diagram shows the change of greeks with respect to chosen x-axis values, holding all other parameters constant
• Click diagram legend to toggle on/off selected greek letters
• Customize the data range by entering Min and Max values in respective boxes
• Use the diagram to practice and develop insights on greek letters - see how the risks and valuation changes with respect to market factor changes