Merton Model

The Merton model is a mathematical model that describes the pricing of options in a market where the underlying asset follows a jump-diffusion process. It was developed by Robert C. Merton in 1973 and is a generalization of the Black-Scholes model.

The Merton model assumes that the underlying asset price follows a geometric Brownian motion with random jumps. The jumps can be either positive or negative, and they can occur at any time. The size of the jumps is determined by a random variable with a specified distribution.

The Merton model is more complex than the Black-Scholes model, but it can be used to price options in more realistic market conditions. For example, the Merton model can be used to price options when the underlying asset is subject to volatility clustering or when the underlying asset is illiquid.

The Merton model is also used to price other financial instruments, such as convertible bonds and credit default swaps.

The Merton model has been criticized for being too complex and for making unrealistic assumptions. However, it remains a valuable tool for pricing options and other financial instruments.

Here are some of the key features of the Merton model:

* The underlying asset price follows a geometric Brownian motion with random jumps.
* The jumps can be either positive or negative, and they can occur at any time.
* The size of the jumps is determined by a random variable with a specified distribution.
* The Merton model can be used to price options in more realistic market conditions.
* The Merton model is also used to price other financial instruments, such as convertible bonds and credit default swaps.