Impact of pricing options on consumer behavior

Price Dynamics

In finance, a price or premium is either paid or received for purchasing or selling certain options. This is typically split into either intrinsic value or time value. Intrinsic value is defined as the difference between the underlying price and the strike price -- or the value in which the option has in the market. Time value is the extra value that compensates for the risk in which the writer/seller undertakes over time. Options, of course, are derivative contracts that give the holder the option (the right) to purchase or sell at a specific price at a specific time (Investopedia, 2013). In economics, prices are a way to measure the value of a good or service through the basis of a security. The overall idea is that in a free market economy, the market price reflects the way supply and demand interacts. In other words, pricing a good or service should equate to the quantity and quality of what the market demands, and then in turn by the marginal utility between different buyers and sellers (e.g. A camel might be worth more in one culture and a first edition book in another). This, of course, may be distorted by government regulations, taxation or tariffs, the environment, and the availability of the service or product (Friedman, 1990).

The Black-Scholes pricing model is a mathematical model that looks at a financial market through derivative investment instruments. This method is popular for options markets and statistical modeling has shown that the BS price is relatively close to the observed price. The model was introduced in 1973 in an academic paper from the Journal of Political Economy. Within this scholarly paper, the authors published a partial differential equation that helps understand the price of options over time. The overall idea behind this theory is to attempt to perfectly hedge the option of buying and selling the asset to attempt to eliminate risk. In the BS theory, this hedge is known as delta hedging and implies that there is actually only one true and correct price for the option (Black & Scholes, 1973). At times, this model is known as the Black-Scholes-Merton model since it was Merton who published a more thorough addition to the model, winning he and Scholes (Black was dead) the 1997 Nobel Prize in Economics (Nobel Foundation, 1997).

In practice, the BS model is used because it is easy to calculate and gives a useful approximation when looking at the direction in which price moves. It is also an important basis for more refined models and is reversible and can be used as an input to other ways to quote option prices. According to most scholarship, it is limited because it underestimates extreme moves, assumes stationary processes with continuous time and trading. This means that while valuable, sometimes the BS model fails to incorporate many market discrepancies and risks (Wilmott, 2008).

The binomial options pricing model (BOPM) provides a way to generalize then numerical value of options. It was first proposed in 1979 and uses a "discrete time" or lattice-based model of the way price varies over time -- without using closed form solutions (Cox, et al., 1979). In actual usage, the BOPM is quite widely used because it handles a wide variety of conditions that other models do not account for -- largely because it is based on the description of an underlying instrument over a longer period of time, as opposed to a single point without a large number of variables. Scholars say that it is computationally slower than the Black-Scholes formula, but more accurate, specifically for longer-dated options on securities that have dividend payments, trade in multiple securities, or have a number of complicated features within their variables. The BOPM model works by tracing the options key underlying variables through a lattice tree, which identifies steps between variables over time. For example, each node in the tree represents a hypothetical (or possible) price at a given point in time, then solves based on a combination of those nodes (Conroy, 2003).