2012Unpublished venueRequires access

Options Pricing and Implied Volatility

Kerry W. Given

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Abstract

This chapter covers the factors that influence the pricing of an option. The Greeks are quantitative measures of the sensitivity of the option's theoretical price to the several variables in the Black-Scholes model. Delta measures how much the option price will change with a $1 move in the underlying stock or index price. Gamma (?) measures how much the value of delta will change with a $1 move in the underlying stock or index price. The Greek theta (?) measures the value of the option's time value that is lost with the passage of one day in time. Vega (V) measures the sensitivity of our option or our option position to changes in implied volatility. If we enter the market price of the option into the Black-Scholes equation and calculate volatility, the result is the volatility “implied” by the market price, or implied volatility. The price of the option will increase as the option has more intrinsic value, more time to expiration, and higher implied volatility.

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This chapter covers the factors that influence the pricing of an option. The Greeks are quantitative measures of the sensitivity of the option's theoretical price to the several variables in the Black-Scholes model. Delta measures how much the option price will change with a $1 move in the underlying stock or index price. Gamma (?) measures how much the value of delta will change with a $1 move in the underlying stock or index price. The Greek theta (?) measures the value of the option's time value that is lost with the passage of one day in time. Vega (V) measures the sensitivity of our option or our option position to changes in implied volatility. If we enter the market price of the option into the Black-Scholes equation and calculate volatility, the result is the volatility “implied” by the market price, or implied volatility. The price of the option will increase as the option has more intrinsic value, more time to expiration, and higher implied volatility.

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Available abstract

This chapter covers the factors that influence the pricing of an option. The Greeks are quantitative measures of the sensitivity of the option's theoretical price to the several variables in the Black-Scholes model. Delta measures how much the option price will change with a $1 move in the underlying stock or index price. Gamma (?) measures how much the value of delta will change with a $1 move in the underlying stock or index price. The Greek theta (?) measures the value of the option's time value that is lost with the passage of one day in time. Vega (V) measures the sensitivity of our option or our option position to changes in implied volatility. If we enter the market price of the option into the Black-Scholes equation and calculate volatility, the result is the volatility “implied” by the market price, or implied volatility. The price of the option will increase as the option has more intrinsic value, more time to expiration, and higher implied volatility.

Key concepts: Implied volatility, Volatility smile, Economics, Black–Scholes model, Call option, Volatility swap, Greeks, Volatility (finance)

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