Nonuniqueness of Option Pricing Under the Meixner Model
Nonuniqueness of Option Pricing Under the Meixner Model
In the classical Black–Scholes model of asset prices, every option has a unique "fair" price; that is, for every price of the underlying asset, there is a unique option price that does not allow arbitrage opportunities. This is no longer true when the Black–Scholes model is replaced by a more realistic model, for example, one in which discontinuous jumps in asset price can occur. This Demonstration shows this for the case where the asset price is modeled by a Meixner process.
There are two plots. In the upper one, the red and pink colored curves show two different models of arbitrage-free option prices based on the same Meixner process describing the underlying asset price. The values shown in red are obtained by means of the Esscher transform applied to the underlying asset process. The pink line shows prices obtained by a change of drift of the underlying process (this is the same method as is used to obtain option prices in the Black–Scholes model). The green line shows the Black–Scholes price for the same variance (volatility). In the lower plot, the user can choose to view the density of the Meixner process model of the (logarithm of) the underlying asset price versus the Black–Scholes (normal) density with the same mean and variance or the "risk-neutral" densities of the two Meixner process models used versus the risk-neutral normal density.