andersen piterbarg interest rate modeling pdf download

An analysis of the fast Fourier transform method revealed that the volatility of volatility σ and the correlation coefficient ρ have significant impact on option values. The comparison of the probability densities of the double exponential jump-diffusion model with stochastic volatility, the Black-Scholes model and the double exponential jump-diffusion model without stochastic volatility showed that the double exponential jump-diffusion model with stochastic volatility has better performance than the two other models with respect to pricing long term options. We developed fast and accurate numerical solutions by means of the Fourier transform method. We derived closed-form solutions for European call options in a double exponential jump-diffusion model with stochastic volatility. This is also obtained by taking the Hilbert transform in the Fourier domain. The fast Hilbert transform method is obtained by multiplying a square integrable function f by an indicator function associated with the barrier feature in the real domain. The fast Fourier transform method utilizes the characteristic function of the underlying instrument’s price process. This paper presents two transform methods for pricing contingent claims namely the fast Fourier transform method and the fast Hilbert transform method. Numerical experiments are conducted using Excel and MATLAB. We illustrate our methodologies by studying the local volatility surfaces of South African index and foreign exchange options. We focus on arbitrage-free conditions, choice of calibrating functionals and selection of numerical algorithms to price options. In this document we discuss various topics that influence the successful construction of implied and local volatility surfaces in practice. Pricing under local volatility has become a field of extensive research in finance and various models are proposed in order to overcome the shortcomings of the Black-Scholes model that assumes the volatility to be constant. Most exotic options on Safex and Yield-X are valued by local volatility models. Exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility.

Many exotic options and even exotic option structures are listed. Investors can negotiate the terms for all option contracts, choosing the type of option, underlying asset and the expiry date. These products give investors the advantages of listed derivatives with the flexibility of ``over the counter' (OTC) contracts. Can-Do Options are derivative products listed on the JSE's derivative exchanges - mostly equity derivative products listed on Safex and currency derivative products listed on Yield-X.

Andersen piterbarg interest rate modeling pdf download