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This paper gives examples of explicit arbitrage-free term structure models with Lévy jumps via the state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a Lévy process is a “natural” scale for the process to be the state...
The Hoggard–Whalley–Wilmott equation is introduced to model portfolios of European type options incorporating transaction costs. The model gives rise to a nonlinear parabolic partial differential equation (PDE), whose nonlinearity reflects the presence of transaction costs. We show analytically...
Lévy processes are popular models for stock price behavior since they allow to take into account jump risk and reproduce the implied volatility smile. In this paper, we focus on the tempered stable (also known as CGMY) processes, which form a flexible 6-parameter family of Lévy processes with...
The HARA and CARA theory of pricing, and the theory of partial, yet the most conservative hedging, of a single (liquid) tradable derivative contract under multidimensionality of risks in incomplete markets, including markets with non-hedgable interest rate risks, was developed by the author in a...
We consider the problem of maximization of expected utility from terminal wealth for log and power utility functions in a market model that leads to purely discontinuous processes. We study this problem as a stochastic control problem both under complete as well as incomplete information. Our...
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