A limit order book provides information on available limit order prices and their volumes. Based on these quantities, we give an empirical result on the relationship between the bid-ask liquidity balance and trade sign and we show that the liquidity balance on the best bid/best ask is quite informative for predicting the future market order’s direction. Moreover, we define price jump as a sell ...

This paper analyzes the equilibrium strategy of a robust optimal reinsurance-investment problem under the mean–variance criterion in a model with jumps for an ambiguity-averse insurer (AAI) who worries about model uncertainty. The AAI’s surplus process is assumed to follow the classical Cramér–Lundberg model, and the AAI is allowed to purchase proportional reinsurance or acquire new business an...

If the intensity parameter in a jump diffusion model is identically zero, then parameters characterizing the jump size density cannot be identified. In general, this lack of identification precludes consistent estimation of identified parameters. Hence, it should be standard practice to consistently pretest for jumps, prior to estimating jump diffusions. Many currently available tests have powe...

We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integrodifferential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time discretization schemes, where the differential (diffusion) term is treated implicitly, while the integral (jump) t...

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...

We consider a limit price of basket options in a large portfolio where the dynamics of basket assets is described as a CEV jump diffusion system. The explicit representation of the limiting price is established using weak convergence of empirical measure valued processes generated by the system. As an application, the closed-form formula of the limit price is derived when the price dynamics of ...

In general, geometric additive models are incomplete and the perfect replication of derivatives, in the usual sense, is not possible. In this paper we complete the market by introducing the so-called power-jump assets. Using a static hedging formula, in order to relate call options and power-jump assets, we show that this market can also be completed by considering portfolios with a continuum o...

In this paper, we provide Laplace transform-based analytical solutions to pricing problems of various occupation-time-related derivatives such as step options, corridor options, and quantile options under Kou’s double exponential jump diffusion model. These transforms can be inverted numerically via the Euler Laplace inversion algorithm, and the numerical results illustrate that our pricing met...

Evaluation of default correlation is an important task in credit risk analysis. In many practical situations, it concerns the joint defaults of several correlated firms, the task that is reducible to a first passage time (FPT) problem. This task represents a great challenge for jump-diffusion processes (JDP), where except for very basic cases, there are no analytical solutions for such problems...