What Is Jump Diffusion?

Jump diffusion is a type of model used to value or price an options contract. It mixes two pricing techniques: the more traditional diffusion model in which factors play out in a smooth and relatively consistent manner, and the jump process model, in which one-off events can cause a major change. The theory is that jump diffusion thus produces a more realistic picture of the way markets behave.

Option pricing is the skill of placing an objective value on an options contract. This is a financial agreement by which one trader buys the right to complete an asset sale or purchase at a fixed price on a future date, but is not forced to complete this exchange. Various models attempt to calculate the different factors that affect how valuable this contract is to the holder. These can include the current price of the underlying asset, the volatility of the asset price, and the time left until the option comes due. Many traders will use a pricing model to decide what price they can pay for an option and get a good balance of value between the money they can make from the option and the risk of it not being worthwhile to exercise the option and thus wasting the purchase price.

The most common forms of option pricing can be described as diffusion based. This works on the basis that market events will have a relatively small effect on asset prices and general trends and patterns will continue. The best known form of diffusion based options pricing is the Black-Scholes model. The main advantage is that such a model can be relatively simple and straightforward to operate.

A contrasting type of model is known as a jump process. This works on the basis that markets do not consistently move in a general smooth direction with small deviations, but rather are much more susceptible to dramatic changes of direction and pace through one-off events. Models using the jump process, such as the binomial options pricing model, attempt to take more account of the potential for unpredictable events. This makes for a more complicated model, though the less time remains until the option comes due, the less disparity there is between the values produced by, for example, Black-Scholes valuations and binomial options valuations.

The economist Robert C. Merton developed a blend of these two models, known specifically as the Merton model, and generally as a jump diffusion model. It attempts to cover the idea that markets have a combination of general trends, minor day-to-day variations, and major shocks. Merton's work on jump diffusion was later incorporated into an adapted Black-Scholes model that won the Novel Prize for economics in 1997.