Option Value with Black-Scholes formula
Originally published: 28/09/2016 16:59
Last version published: 24/01/2017 15:49
Publication number: ELQ-76537-4
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Option Value with Black-Scholes formula

Find the value of puts, calls, and combinations of options using the Black-Scholes formula.

The formal evaluation of options exploits the principles of complete markets and the risk-less arbitrage to deduce that investors in options should be neutral to risk.

Hence, the option pricing model below used risk-neutrality as a given and assumes that the risk of the underlying asset is described in a normal distribution.

This is adapted from "An Introduction to Options, Entrepreneurial Finance" by Janet Kilholm SMith, Richard L. Smith and Richard T. Bliss

This Best Practice includes
1 Excel Model

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Further information

Required input data:
- Stock Price now
- Exercise Price of Option
- Number of periods to Exercise in years
- Compounded Risk-Free Interest Rate
- Standard Deviation

Produced output:
- Present Value of Exercise Price
- s*t^.5
- d1
- d2
- Delta N(d1) Normal Cumulative Density Function
- Bank Loan N(d2)*PV(EX)

- Value of Call
- Value of Put

The Option Pricing Model depends on market completeness, continuous trading, normally distributed risk, independence, and other factors to derive option values. When these assumptions are violated (as they usually are for new ventures and for real options), formal valuation approaches can still provide insights, but the actual values of options are less certain. It is common to employ simulation and numerical methods to value options when critical assumptions are not satisfied"

(An Introduction to Options, Entrepreneurial Finance, by Janet Kilholm SMith, Richard L. Smith and Richard T. Bliss)

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