Black-Scholes Merton Model Calculator (With Greeks), Option Strategies Layout and Delta Hedging Calculator
Originally published: 07/04/2020 09:13
Last version published: 07/04/2020 12:42
Publication number: ELQ-61850-2
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Black-Scholes Merton Model Calculator (With Greeks), Option Strategies Layout and Delta Hedging Calculator

This model can be used by students and professionals to determine the value of options, and specific trading strategies.

The Black-Scholes Merton Model is a mathematical formula used to derive the estimated price of call and put options. The standard BSM model is used to calculate the price of European options, where the option may only be exercised at its expiry date. The following Greeks are calculated and graphed in the "BSM Calculator" sheet: Delta, Gamma, Vega, Theta, Rho.

The "Options Strategies" Sheet examines the most widely used option strategies. The model calculates the various payoff metrics for the following strategies:

- Long/Short Calls
- Long/Short Puts
- Bull/Bear Spreads
- Butterfly Spreads (with both calls and puts)
- Zero-Cost Collar
- Straddle

Fill in the blue text columns to adjust each variable, and time increments on the graph. Use the drop-down menu to select among each option strategy where applicable. Each strategy will have its own value/profit at expiration, underlying price, strike price, and option premium.

The "Delta Hedging" sheet looks at a strategy dealers and complex option traders use to hedge their positions. The calculator will 1) determine the appropriate amount of underlying to purchase at inception, and 2) adjust the total position in order to remain delta hedged. The call price is determined using the BSM model. Fill in the blue text areas to adjust the dynamics of the model.

It is important to recognize the limitations of the BSM model: the further out of the money the option is, the less-valuable the approximate of delta. BSM also assumes the distribution is asymmetric.

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Further information

To discover how option prices are derived, as well as an in-depth understanding of the factors that influence option pricing (i.e. The Greeks). Furthermore, this model will help users understand the payoff metrics of multiple option strategies, and gain additional info on how option strategies can be delta-hedged.

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