Option Greeks Calculator 32.0.0

The Option Greeks Calculator employs the latest advancements of the Black-Scholes model to provide precise theoretical pricing for European call and put options, along with their associated Greeks. Users may input the underlying asset price manually or retrieve it from various global exchanges via a fetching feature; however, it is important to note that there may be delays of up to 15 minutes for fetched prices. Subsequent inputs include Exercise Price, Days Until Expiration, Interest Rates (%), and Volatility (%). The exclusion of yield considerations aims to maintain simplicity and clarity in the calculations.

The Black-Scholes model, foundational to modern options pricing, facilitates a theoretical estimation of European-style options prices. Its introduction significantly stimulated options trading and validated the operations of markets such as the Chicago Board Options Exchange. Despite frequent adjustments, the model remains widely utilized within the financial community, with empirical tests demonstrating that Black-Scholes prices typically align closely with observable market prices.

This application calculates theoretical prices and Greeks with high precision, utilizing 16 decimal accuracy for d1, d2, call, and put prices through cumulative and standard normal distributions. For user-friendliness, these values are rounded to three decimal places.

Key assumptions of the Black-Scholes Model include:

1. The stock does not pay dividends during the life of the option
2. The model applies strictly to European exercise terms
3. Market conditions are efficient
4. No commissions are involved
5. Interest rates remain constant and known throughout
6. Returns are lognormally distributed

The formulas utilized are as follows:

c = S + p – Xe^-r(T-t)

p = c – S + Xe^-r(T-t)

Where:

• c = call value
• S = current stock price
• p = put price
• X = exercise price
• e = Euler's constant (approximately 2.71828)
• r = continuously compounded risk-free interest rate
• T = expiration date
• t = current date value

The Option Greeks incorporated in this calculator include:

1. Delta - measures the change in option value relative to fluctuations in the underlying asset price.
2. Vega - assesses sensitivity to volatility changes in the underlying asset.
3. Theta - quantifies the sensitivity of an option's value over time.
4. Rho - evaluates sensitivity to interest rate variations.
5. Gamma - analyzes changes in Delta as related to variations in the underlying asset price.

Disclaimer: While every effort is made to ensure accuracy in output from the Option Greeks Calculator, users should exercise caution; we are not liable for any losses arising from inaccuracies or any other issues. All information provided is intended solely for informational purposes and should not be considered investment advice.

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