# HP 30b Black-Scholes Equation

The HP 30b implement the Black-Scholes Equation which has been used extensively in option markets worldwide since its publication in 1973. It is a way to find out how much a call option is worth at any given time. The Black-Scholes Equation operated on the theory that that an investor can precisely replicate the payoff to a call option by buying the underlying stock and financing part of the stock purchase by borrowing. The formula was groundbreaking because it was the first of its kind that actually worked, due to the fact that it eliminated variables that were impossible to measure, such as 'investor fear', that other formulas carried.

The five inputs are simply keyed into the five financial variables and then the HP 30b displays the call option value, and the put option value. The program must be given the following parameters: the exercise price, the risk-free rate, the time to expiration, and the price and volatility of the underlying stock.

Example 1, Part 1: An option has 6 months to run and a strike price of $45. Find Call and Put values assuming a spot price of $52, return volatility of 20.54% per month and a risk-free interest rate of 0.5% per month.

To invoke Black-Sholes on the HP 30b, press & hold [Shift] and [Black S] keys together.

Stock (Spot/Current) Price (S) = Enter **52** press [INPUT] [Down Arrow]

Strike Price (X) = Enter **45** press [INPUT] [Down Arrow]

Time to Maturity (T) = Enter **6** (months) press [INPUT] [Down Arrow]

Risk Free % interest rate (r) = Enter **0.5** (% per month) press [INPUT] [Down Arrow]

Rate of Return % Volatility Assumption (v) = Enter **20.54** press [INPUT] [Down Arrow]

Dividend % = Press [Down Arrow], to ignore.

HP 30b Computed Results: Use [Down Arrow] to retrieve.

Call (Value) Price = **14.22**

Put (Value) Price = **5.89**

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Example 1, Part 2: Use the above example data, but show how to re-scale the data to use a yearly time unit.

To invoke Black-Sholes on the HP 30b, press & hold [Shift] and [Black S] keys together.

Press [Down Arrow] [Down Arrow]

Time to Maturity (T) = 6 (months) /12 = Enter **0.5** (year) press [INPUT] [Down Arrow]

Risk Free % rate (r) = 0.5 x 12 = Enter **6** (% per year) press [INPUT] [Down Arrow]

Rate of Return % Volatility (v) = 20.54 x sqrt(12) Enter **71.15** press [INPUT] [Down Arrow]

Dividend % = Press [Down Arrow], to ignore.

HP 30b Computed Results: Use [Down Arrow] to retrieve.

Call Price = **14.22**

Put Price = **5.89**

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Example 2: The stock price six months from the expiration of an option is $42, the exercise price of the option is $40, the risk-free interest rate is 10% per annum, and the volatility is 20% per annum. Find Call and Put values.

To invoke Black-Sholes on the HP 30b, press & hold [Shift] and [Black S] keys together.

Stock (Spot) Price (S) = Enter **42** press [INPUT] [Down Arrow]

Strike Price (X) = Enter **40** press [INPUT] [Down Arrow]

Time to Maturity/Expiry (T) = Enter **0.5** (year) press [INPUT] [Down Arrow]

Risk Free/Interest % rate (r) = Enter **10** (% per year) press [INPUT] [Down Arrow]

Rate of Return % Volatility (v) = Enter **20** (% per year) press [INPUT] [Down Arrow]

Dividend % = Press [Down Arrow], to ignore.

HP 30b Computed Results: Use [Down Arrow] to retrieve.

Call (Value) Price = **4.76**

Put (Value) Price = **0.81**

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Updated On: 10.01.08