Opion Implied Volatility Calculator for European options (Black-Scholes Model)

What are the basic option terms I need to know?

Spot price: The spot price refers to the price of the underlying upon which the option is based. The underlying may be a stock, a commodity, currency etc. 

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Strike price: The strike price is the price at which the buyer (seller) has the right to buy (sell) the underlying to the seller (buyer) of the option. In the case of call options, the buyer has the right to buy the underlying at the strike from the call option seller. In the case of put options, the buyer has the right to sell the underlying at the strike price to the put option seller. 

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Days to expiry: Days to expiry refers to the number of days in which the call or put option will expire.

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Option price: The option price refers to the price of a given option. In this calculator, we are calculating the implied volatility for a given price. One can either input the spot price or another (expected) price in order to compute what the implied volatility of the option is.

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Implied volatility: Implied volatility refers to the volatility of an option such that when input into the Black-Scholes Model results in an option price equal to that of the market price.

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What are the formulas used in this options implied volatility calculator?

This implied volatility calculator uses the formulas from the Black-Scholes Model mentioned above.

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Why do I need to know the implied volatility of an option?

The price of an option is not constant over its lifespan. While other factors such as the risk free interest rate play a role, the main influencing variables are the price of the underlying and the days to expiry. However, sometimes the price of an option does not change even when the price of the underlying and/or the days to expiry changes. Sometimes the price of an option increases or decreases even though the price of the underlying has not changed and if we neglect time. It is also possible that the underlying price doesn't change, but the option price increases even though days to expiry reduces. If the price of the option is assumed to be the fair price, then these situations can be traced to a change in the volatility of the option. As the option price is a function of what the market as a whole expects, knowing what volatility is implied at a given price becomes useful chiefly while designing option strategies, managing risk etc. As a rule, if the implied volatility increases, ceterus paribus, then the price of the call or put option will increase as well. If the price of the option remains constant but the days to expiry reduces, then the implied volatility would have to increase such that the theta of the option is offset by the corresponding price increase.

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What does this option volatility calculator do?

This calculator uses the inputs: days to expiry, underlying price, option strike price, the risk free interest rate and the option price to calculate the implied volatility of a European option. This is done by iteratively solving the equation for the fair price of an option to determine the implied volatility. In this calculator, the impact of the dividend yield is neglected.

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Why is this calculator useful?

This option volatility calculator is useful as it helps calculate the implied volatility of an option. One could theoretically use an option pricing calculator by changing the volatility input such that the option price matches the current spot price but that can be slightly time consuming as a bit of trial and error is needed. This calculator eliminate that by directly solving for implied volatility.

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How do I use this option volatility calculator?

Instructions to use this option volatility calculator are provided above.