Transform Analysis and Asset Pricing for Affine Jump-diffusions

Abstract

In the setting of ‘affine’ jump‐diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed‐income pricing models, with a role for intensity‐based models of default, as well as a wide range of option‐pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.

Good and Bad Variance Premia and Expected Returns

“…One can also enrich the model by separating volatility and jump risk factors, consistent with the findings in Santa-Clara and Yan (2010), and incorporating additional volatility-related factors, such as the long-run volatility (see Duffie, Pan, and Singleton (2000)), or volatility of volatility (see Bollerslev, Tauchen, and Zhou (2009)). Further, for simplicity, the two jump intensities are assumed to be uncorrelated in our framework.…”

Mean-variance hedging with oil futures

“…This follows from the results on affine term structure models in [9]. For completeness, we give the proof in the appendix.…”

Revealing the implied risk-neutral MGF from options: The wavelet method

“…For instance, the classic Black and Scholes model assumes that the stock prices follow the Geometric Brownian motion with a constant risk-free rate and constant volatility implying a lognormal distribution for the stock prices. Other examples include Duffie et al (2000) and Bates (2000) for the jump-diffusion process and stochastic volatility model.…”