Question 1

What is the Black-Scholes model and how does it price options?

Accepted Answer

The Black-Scholes model is a mathematical formula for pricing European-style options, published by Fischer Black, Myron Scholes, and Robert Merton in 1973. It assumes the underlying asset follows a log-normal distribution of returns, a constant risk-free rate, no dividends (in the basic form), and no transaction costs. The model outputs a fair value for a call or put option given five inputs: the current stock price, the strike price, time to expiration, the risk-free interest rate, and implied volatility. It remains the industry standard for initial option pricing despite its assumptions being simplifications of real markets.

Question 2

What are the option Greeks and what does each measure?

Accepted Answer

The Greeks measure how an option's price changes as market conditions shift. Delta is the change in option price per one-unit move in the underlying - a call delta of 0.6 means the option gains $0.60 for each $1 rise in the stock. Gamma is the rate of change of delta, showing how delta itself accelerates. Vega measures sensitivity to a one-percentage-point change in implied volatility. Theta is the daily time decay - how much value the option loses each day as expiration approaches. Rho measures sensitivity to a one-percentage-point change in the risk-free rate, which is typically small for short-dated options.

Question 3

What is implied volatility and how does it affect option pricing?

Accepted Answer

Implied volatility (IV) is the market's forward-looking estimate of how much the underlying asset will move, expressed as an annualised percentage. Unlike historical volatility, which looks backward, IV is derived by working the Black-Scholes formula in reverse: given a market option price, what volatility assumption produces that price? Higher IV raises both call and put prices because a larger expected move increases the probability of the option finishing in the money. When IV spikes - as it does before earnings or macro events - options become significantly more expensive even if the underlying price has not changed.

Question 4

What is the difference between a call and a put option?

Accepted Answer

A call option gives the buyer the right, but not the obligation, to purchase the underlying asset at the strike price before expiration. Calls profit when the underlying price rises above the strike. A put option gives the buyer the right to sell the underlying at the strike price. Puts profit when the underlying falls below the strike. Buying a call is a bullish bet; buying a put is a bearish bet or a hedge against a long position. Both have limited downside equal to the premium paid and, for calls, theoretically unlimited upside.

Question 5

Is the Option Pricing Calculator on Worthmap free?

Accepted Answer

Yes. The Worthmap Option Pricing Calculator is completely free and requires no account. Enter the stock price, strike price, days to expiration, risk-free rate, and implied volatility to instantly get Black-Scholes prices for both the call and the put, along with full Greeks: Delta, Gamma, Vega, Theta, and Rho. The calculator runs entirely in your browser - no data is stored or sent to a server.

Option Pricing Calculator - Black-Scholes & Option Greeks