The Heath-Jarrow-Morton framework ("HJM") is a general framework to model the evolution of interest rate curve - instantaneous forward rate curve in particular (as opposed to simple forward rates) The key to these techniques is the recognition that the drifts of the no-arbitrage evolution of certain variables can be expressed as functions of their volatilities and the … [Read more...]
Heston model: The Overview
The Heston model is a mathematical model describing the evolution of the volatility of an underlying asset . It is a stochastic volatility model: such a model assumes that the volatility of the asset is not constant, nor even deterministic, but follows a random process. n the Heston model, we still have one asset (volatility is not considered to be directly observable or … [Read more...]
Variance Gamma Model: Overview
The variance-gamma distribution is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the gamma distribution. The most widely used option pricing model is the Black-Scholes model. We motivate an alternative option pricing model called the Variance Gamma (VG) model and demonstrate its implementation in the … [Read more...]