In this paper we extend a reduced form model for the valuation of employee share options (ESOs) to incorporate employee departure, and company takeover. We also allow for performance linked vesting and other exotic features specific to ESOs. We clarify the assumptions underlying the reduced form...

We investigate the valuation and hedging of catastrophe options, whose claim arrival process is modeled by the Cox process or a doubly stochastic Poisson process. Employing the non-arbitrage principle we obtain closed form formula for the pricing of the option. Various hedging parameters are...

We consider a supercritical branching population, where individuals have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant rate. We assume that individuals independently experience neutral mutations, at constant rate θ during...

Reduced form credit risk models are important ones in credit risk theory. In such a model, certain correlated relations are constructed to represent the default dependence structure among the default intensity processes. In this paper, we introduced a reduced form credit risk model in which the...

We propose a flexible framework for pricing single-name knock-out credit derivatives. Examples include Credit Default Swaps (CDSs) and European, American and Bermudan CDS options. The default of the underlying reference entity is modelled within a doubly stochastic framework where the default...

This research attempts to propose closed-form solutions for prices of credit-risky bonds, assuming a nonzero correlation between interest rates and credit spreads. The times of default of a credit-risky bond are modelled as the jump times of a Cox process, following the method of Lando, with an...

Relative intra-day cumulative volume is intra-day cumulative volume divided by final total volume. If intra-day cumulative volume is modeled as a Cox (doubly stochastic Poisson) point process, then using initial enlargement of filtration with the filtration of the Cox process enlarged by...

The aim of this paper is to provide a new approach to project the Mortgage Backed Securities (MBS) cash flows in emerging markets where collateral information is limited, wrong or scarce. Under this framework, we use the Cox Process to model stochastic probabilities of prepayment and default....