Black and Scholes for the HP12c
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VoyagerPack1
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214.94 €
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199.99 €
12c Financial Calculator
69.95 €
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64.95 €
In stock
The HP12c has been the standard weapon of choice for most financial positions in Wall Street for many years. Its mix of a good function set and an unmatched way of doing operations with it were paramount in an environment where decisions had to be made quick. However, since a long time ago, most of the calculations are done on spreadsheets since it provides backup and allows for much more complex calculations. Enter Black and Scholes formula.
The Black-Scholes model (often just called Black-Scholes) is a groundbreaking mathematical framework developed in 1973 by economists Fischer Black, Myron Scholes, and Robert Merton. It revolutionized options trading by providing a way to calculate the fair price of European-style options—financial derivatives that give the buyer the right (but not the obligation) to buy or sell an underlying asset (like a stock) at a predetermined price (strike price) on a specific expiration date.
Before Black-Scholes, options pricing was more art than science, relying on guesswork. This model made it a precise, quantitative tool, earning Scholes and Merton the 1997 Nobel Prize in Economics (Black had passed away by then).
Key Assumptions
The model simplifies reality with these core assumptions:
- European options only: Can only be exercised at expiration (not early, unlike American options).
- Efficient markets: Stock prices follow a random walk (geometric Brownian motion), with no arbitrage opportunities.
- Constant volatility: The underlying asset's price volatility (σ) stays the same over time.
- Risk-free rate: There's a constant, known risk-free interest rate (r), like from government bonds.
- No dividends: The underlying asset pays no dividends during the option's life.
- No transaction costs or taxes: Trading is frictionless.
- Log-normal distribution: Stock prices can't go negative and tend to drift upward over time.
In practice, these don't always hold (e.g., volatility changes), but the model is still widely used as a benchmark.
There is a well known program for Black and Scholes with detailed explanations that you can find here:
https://www.hpcalc.org/details/9734
If you have downloaded the latest version of HP12c's firmware, you can upload to your HP12c this file:
(using VoyagerInterface for Windows or Mac)
