# Introduction To Options Pricing And Theoretical Value

Before we can fully understand the risk reward for our stock option combination trading strategies, we need a way to quantify the impact of different option trades.

Determining stock trading profitability is easy, as you simply subtract the last price from the trade price and multiply that by the quantity traded.

But options trading, and the tremendous flexibility it allows, including what are called synthetic stock trades and a way to trade stock using options – also leads to trading math that is more complicated than stock trading alone.

Our options trading spreadsheet is important to our option trading strategies, because it allows us a way to model the risk and reward to a trade or to a change in an existing position.

Especially important is the ability to be able to project a given option price, or its theoretical value, as a result of changes in the following:

• The price of the underlying
• Implied volatility
• Passage of time

This is done by using the pricing model built into the options spreadsheet.

I want to further discuss these important components, and what is referred to as the ‘greeks’, that are derived from the option pricing formula, along with using the different option trading worksheets.

The option ‘greeks’ come from the same option pricing model that is used to determine the theoretical value – our option trading spreadsheet uses the Black-Scholes model.

Along with theoretical value, there are other ‘greeks’ that are important for our trading strategies:

• Delta
• Theta
• Vega
• Implied volatility

NOTE:  Gamma and Rho are also derived from the pricing model, but they are not as much of a concern for our trading.

Theoretical value and a way to project an option price is determined by the options pricing model, using the following inputs in the formula:

• Option type
• Underlying price
• Option strike
• Days to expiration
• Risk free interest rate
• Volatility

NOTE:  By using the actual option price as a formula input, along with the other pricing components [except volatility], the implied volatility of the option can be determined – for our trading and projections, implied volatility is used as our volatility input.

You are now looking at a print from the spreadsheet worksheet that is used for determining the ‘greeks’ and implied volatility. The blue cells that you see are where the necessary formula components are entered – and the remaining cells include the formulas.

You will also note that the first column has nothing entered, while the remaining columns have the inputs, greeks and implied volatility filed in – I want to show you an example of some of the ways we can use this worksheet to do different projections for theoretical value.

The first 2 columns start on 9/12, with an expiration of 9/20, for a 45 strike call and put when the underlying is 45.00.  I started with the actual option price from my quotes, to get the implied volatility and the volatility input.

Now look at the next 2 columns. We are now doing a whatif – for what the option prices will be on the next day, with an underlying move from 45 to 46, and a change in the implied volatility.

Columns 5 and 6 do the same thing – but in this case we are solving for a move down in the underlying price, from 45 to 44.

We will be going into the spreadsheet and go through the actual usage and inputs for the worksheet, after discussing more about the output from the options pricing formula.