How to Calculate Options Prices and Their Greeks: Exploring the Black Scholes Model from Delta to Vega

Chapter 6Pricing

In this chapter we will briefly discuss the pricing of the model. There is a very simple rule of thumb to price at the money options. At the money straddles (calls and puts of the same strike) will be valued first; later, the value of this straddle will be used as a sort of standard deviation in the pricing of other options in order to compute the value and Greeks of option combinations and spreads.

As shown before, the standard deviation of a Future is . This implies that with a volatility of 10% (annualised) and the future at 50, in a year's time the Future will trade somewhere between 45 and 55 with a 68% probability and between 40 and 60 with a 95% probability. If the time would double, the standard deviation will become , being around $7 as a standard deviation with a 68% probability for the Future to trade somewhere between 43 and 57 and a 95% probability for the Future to trade somewhere between 36 and 64. With volatility at 15%, time to maturity 1 year and the Future at 50, the standard deviation will be 7.50 and so on.

With regards to option theory, the value of the at the money straddle can be applied as a sort of standard deviation which will be of great help in computing the value of options prices and their Greeks. As shown in the former chapter, the ...