International Journal of Theoretical and Applied Finance

We study the sensitivity of European option prices with respect to correlation parameters in the multi-asset Heston model. The differentiability of the price function with respect to the correlation is proved by using the regularity of the flow of the Cox–Ingersoll–Ross model. In the bidimensional case and when the Feller condition is satisfied, we establish an asymptotic approximation for the derivative of the price with respect to the correlation for short maturities. This approximation is used to discuss monotony issues for exchange and spread option prices. Monotony properties are also obtained for some values of "the volatility of the volatility parameter" and of the correlation between stock prices and their volatilities. We conclude with a large number of simulations that confirm the theoretical results.

We study the behavior of the long-term yield in a HJM setting for forward rates driven by Lévy processes. The long-term rates are investigated by examining continuously compounded spot rate yields with maturity going to infinity. In this paper, we generalize the model of Karoui et al. (1997) by using Lévy processes instead of Brownian motions as driving processes of the forward rate dynamics, and analyze the behavior of the long-term yield under certain conditions which encompass the asymptotic behavior of the interest rate model's volatility function as well as the variation of the paths of the Lévy process. One of the main results is that the long-term volatility has to vanish except in the case of a Lévy process with only negative jumps and paths of finite variation serving as random driver. Furthermore, we study the required asymptotic behavior of the volatility function so that the long-term drift exists.

In this paper, we propose a novel, analytically tractable, one-factor stochastic model for the dynamics of credit default swap (CDS) spreads and their returns, which we refer to as the spread-return mean-reverting (SRMR) model. The SRMR model can be seen as a hybrid of the Black–Karasinski model on spreads and the Ornstein–Uhlenbeck model on spread returns, and is able to capture empirically observed properties of CDS spreads and returns, including spread mean-reversion, heavy tails of the return distribution, and return autocorrelations. Although developed for modeling CDS spreads, the SRMR model has applications for many other stochastic processes with similar empirical properties, including more general rate processes.

We pursue an inverse approach to utility theory and associated consumption and investment problems. Instead of specifying a utility function and deriving the actions of an agent, we assume that we observe the actions of the agent (i.e. consumption and investment strategies) and ask if it is possible to derive a utility function for which the observed behavior is optimal. We work in continuous time both in a deterministic and stochastic setting. In the deterministic setup, we find that there are infinitely many utility functions generating a given consumption pattern. In the stochastic setting of a geometric Brownian motion market it turns out that the consumption and investment strategies have to satisfy a consistency condition (PDE) if they are to come from a classical utility maximization problem. We show further that important characteristics of the agent such as risk attitudes (e.g., DARA) can be deduced directly from the agent's consumption and investment choices.

We study pricing equations in jump-to-default models, and we provide conditions under which the option price is the unique classical solution, with a special focus on boundary conditions. In particular, we find precise conditions ensuring that the option price at the default boundary coincides with the recovery payment. We also study spatial convexity of the option price, and we explore the connection between preservation of convexity and parameter monotonicity.

The paper discusses the pricing of derivatives using a stochastic discount factor modeled as a regime switching geometric Brownian motion. The regime switching is driven by a continuous time hidden Markov chain representing changes in the economy. The stochastic discount factor enables to define a risk neutral measure. We model the stock price as discounted future dividends driven by the same continuous time Markov chain. The stochastic discount factor is used to price European style options under the historical probability measure. The introduction of occupation times of the Markov chain and the corresponding conditional characteristic function allows the evaluation of the expected value of European type claims. The option price is given as a semi-analytical form using the Fourier transform.

Recent empirical studies have demonstrated the informative nature of the equity returns in explaining the variation of the underlying firm's credit default swap (CDS) spreads. Motivated by these findings, we propose a unified credit-equity model by extending the latent structural model in Kijima et al. (2009). As in the original latent model, we treat the actual status of the firm to be unobservable and one can extract information from the marker process that is observable to the investors. Default occurs when the actual firm value drops below a default threshold for the first time. Different from the model in Kijima et al. (2009), however, we define the marker process to be the firm's equity process. Choosing firm's equity process to be a marker process subsequently relaxes the restrictions imposed in Kijima et al. (2009), enabling us to price firm-related securities.

Additionally, we enrich the original latent structural model with jump and regime-switching dynamics. The purpose of the extensions is to capture more realistic credit spreads and implied volatility skews under different economic environments. The proposed model maintains analytical tractability even under such complex dynamics, for the prices of CDSs and equity options admit semi-closed-form solutions. In sum, our model can evaluate corporate securities and their derivatives in a unified framework.