In the execution cost problem, an investor wants to minimize the total expected cost and risk in the execution of a portfolio of risky assets to achieve desired positions. A major source of the execution cost comes from price impacts of both the investor’s own trades and other concurrent institutional trades. Indeed price impact of large trades have been considered as one of the main reasons fo...

This paper treats jump-diffusion processes in continuous time, with emphasis on the jump-amplitude distributions, developing more appropriate models using parameter estimation for the market in one phase and then applying the resulting model to a stochastic optimal portfolio application in a second phase. The new developments are the use of uniform jump-amplitude distributions and time-varying ...

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering limiting models for our resulting approximating GARCH-Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffus...

In this paper we investigate the recently documented trading profits based on technical trading rules in an asset pricing framework that incorporates jump risk and time-varying risk premia. Following Brock, Lakonishok, and LeBaron (1992), we apply popular technical trading rules to the daily S&P 500 index over a long period of time. Trading profits are examined using bootstrap simulation to add...

There is strong evidence that structural models of credit risk significantly underestimate both credit yield spreads and the probability of default if the value of corporate assets follows a diffusion process. Adding a jump component to the firm value process is a potential remedy for the underestimation. However, there are very few empirical studies of jump-diffusion (or Levy) structural model...

In pricing and hedging with financial derivatives, term structure models with jump are particularly important [1], since ignoring jumps in financial prices may cause inaccurate pricing and hedging rates [2]. Solutions of term structure model under jump-diffusion processes are justified because of movements in interest rates displaying both continuous and discontinuous behaviors [3]. Moreover, t...

This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, si...

The jump diffusion process has come to play an important role in many branches of science and industry. In their book [25], Øksendal and Sulem have studied the optimal control, optimal stopping and impulse control for jump diffusion processes. In mathematical finance theory, many researchers have developed option pricing theory, for example, Merton [24] was the first to use the jump process to ...