Abstract: This chapter starts by deriving the Black-Scholes (B–S) differential equation for the price of an option. The B-S model is one of the most important models in the evolution of the quantitative finance. The Heston model is a stochastic volatility model that assumes that the volatility of the asset is non-constant and follows a random process. The SABR model is a stochastic volatility model, which is used to capture the volatility smile in derivatives markets and also used in the forward rate modeling of fixed income instruments. Cox–Ingersoll–Ross model is typically used to describe the evolution of interest rates. The Local volatility models are widely used in the financial industry to hedge barrier options. The chapter presents an example of calculating the implied volatility using the Newton's method. In spline approximation method the local volatility function is obtained using a bicubic spline approximation which is computed by solving an inverse box-constrained nonlinear optimization problem.
Publication Year: 2019
Publication Date: 2019-11-04
Language: en
Type: other
Indexed In: ['crossref']
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