Real options maximizing survival probability under incomplete markets

By integrating the survival problem into the theory of real option valuation under incomplete markets, we analyze an entrepreneurial firm's optimal survival probability and the joint decisions of business investments and portfolio choices when the business investment opportunity has undiversifiable idiosyncratic risks. Based on the theory of stochastic control, we derive the semi-closed-form solutions for the firm's optimal survival probability, its investment thresholds and the implied option value. The results show that the goal of maximizing the survival probability greatly changes the entrepreneur's business investment strategies, the pattern of asset allocation and the correlation between the option value and the project risks. The comparative statics analysis shows that public authorities should subsidize entrepreneurs and maintain stabile financial markets in order to encourage entrepreneurship.     

Pricing swing options in the electricity markets under regime-switching uncertainty

The spot price market for electricity is highly volatile. The time series of the daily average electricity price is characterised by seasonality, mean reversion, jumps, and regime-switching processes. In electricity markets, ‘swing’ contracts, which can provide some protection against the day-to-day price fluctuations, are used to incorporate flexibility in acquiring given quantities of electricity. We develop a lattice approach for the valuation of swing options by modelling the daily average price of electricity by a regime-switching process that utilises three regimes, consisting of Brownian motions and a mean-reverting process. Various numerical examples are presented to illustrate the methodology.     

Real options under a double exponential jump-diffusion model with regime switching and partial information

We consider the irreversible investment in a project which generates a cash flow following a double exponential jump-diffusion process and its expected return is governed by a continuous-time two-state Markov chain. If the expected return is observable, we present explicit expressions for the pricing and timing of the option to invest. With partial information, i.e. if the expected return is unobservable, we provide an explicit project value and an integral-differential equation for the pricing and timing of the option. We provide a method to measure the information value, i.e. the difference between the option values under the two different cases. We present numerical solutions by finite difference methods. By numerical analysis, we find that: (i) the higher the jump intensity, the later the option to invest is exercised, but its effect on the option value is ambiguous; (ii) the option value increases with the belief in a boom economy; (iii) if investors are more uncertain about the economic environment, information is more valuable; (iv) the more likely the transition from boom to recession, the lower the value of the option; (v) the bigger the dispersion of the expected return, the higher the information value; (vi) a higher cash flow volatility induces a lower information value.     

Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model

This paper develops two novel methodologies for pricing and hedging European-style barrier option contracts under the jump to default extended constant elasticity of variance (JDCEV) model, namely: a stopping time approach based on the first passage time densities of the underlying asset price process through the barrier levels; and a static hedging portfolio approach in which the barrier option is replicated by a portfolio of plain-vanilla and binary options. In doing so, both valuation methodologies are extended to a more general set-up accommodating endogenous bankruptcy, time-dependent barriers and the commonly observed stylized facts of a positive link between default and equity volatility and of a negative link between volatility and stock price. The two proposed numerical methods are shown to be accurate, easy to implement and efficient under both the JDCEV model and the nested constant elasticity of variance model.     

A closed-form solution to American options under general diffusion processes

This paper investigates American option pricing under general diffusion processes. Specifically, the underlying asset price is assumed to follow a diffusion process in which both the dividend yield and volatility are functions of time and the underlying asset price. Using the generalized homotopy analysis method, the determination of the early exercise boundary is separated from the valuation procedure of American options. Then, an exact and explicit solution for American options on a dividend-paying stock is derived as a Maclaurin series. In addition, the corresponding optimal early exercise boundary and the Greeks are obtained in closed-form solutions. A nonlinear sequence transformation, the Padé technique, is used to effectively accelerate the convergence of the partial sums of the infinite series. As the homotopy constructed in this paper is based on a generalized deformation with a shape parameter and kernel function, the error of the homotopic approximation could be reduced further for a fixed order. Numerical examples demonstrate the validity, effectiveness, and flexibility of the proposed approach.