Model‐based quantification of the volatility of options at transaction level with extended count regression models

In this paper, we elaborate how Poisson regression models of different complexity can be used in order to model absolute transaction price changes of an exchange‐traded security. When combined with an adequate autoregressive conditional duration model, our modelling approach can be used to construct a complete modelling framework for a security's absolute returns at transaction level, and thus for a model‐based quantification of intraday volatility and risk. We apply our approach to absolute price changes of an option on the XETRA DAX index based on quote‐by‐quote data from the EUREX exchange and find that within our Bayesian framework a Poisson generalized linear model (GLM) with a latent AR(1) process in the mean is the best model for our data according to the deviance information criterion (DIC). While, according to our modelling results, the price development of the underlying, the intrinsic value of the option at the time of the trade, the number of new quotations between two price changes, the time between two price changes and the Bid–Ask spread have significant effects on the size of the price changes, this is not the case for the remaining time to maturity of the option. Copyright © 2006 John Wiley & Sons, Ltd.     

Currency options as theoretical and practical instrument in hedging the exchange risk in excess of loss reinsurance

The paper demonstrates that a ceding company can fully hedge itself against adverse movements of the exchange rate in the case of excess of loss foreign reinsurance by using the currency option markets.     

Flexible waste management under uncertainty

In this paper, we use stochastic dynamic programming to model the choice of a municipality which has to design an optimal waste management program under uncertainty about the price of recyclables in the secondary market. The municipality can, by undertaking an irreversible investment, adopt a flexible program which integrates the existing landfill strategy with recycling, keeping the option to switch back to landfilling, if profitable. We determine the optimal share of waste to be recycled and the optimal timing for the investment in such a flexible program. We find that adopting a flexible program rather than a non-flexible one, the municipality: (i) invests in recycling capacity under circumstances where it would not do so otherwise; (ii) invests earlier; and (iii) benefits from a higher expected net present value.     

Fixed versus flexible production systems: A real options analysis

In this work, we address investment decisions in production systems by using real options. As is standard in literature, the stochastic variable is assumed to be normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. The methodology establishes a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case) and then, computes the project value. We have developed and implemented stochastic dynamic programming models both for fixed and flexible capacity systems. In the former case, we consider three standard options: the option to postpone investment, the option to abandon investment, and the option to temporarily shut-down production. For the latter case, we introduce the option of corrective action, in terms of production capacity, that the management can take during the project by considering the existence of one of the following: (i) a capacity expansion option; (ii) a capacity contraction option; or (iii) an option considering both expansion and contraction. The full flexible capacity model, where both the contraction and expansion options exist, leads, as expected, to a better project predicted value and thus, investment policy. However, we have also found that the capacity strategy obtained from the flexible capacity model, when applied to specific demand data series, often does not lead to a better investment decision. This might seem surprising, at first, but it can be explained by the inaccuracy of the binomial model. The binomial model tends to undervalue future decreases in the stochastic variable (demand), while at the same time tending to overvalue an increase in future demand values.     

Investment timing and optimal capacity choice for small hydropower projects

This paper presents a method for assessing small hydropower projects that are subject to uncertain electricity prices. We present a real options-based method with continuous scaling, and we find that there is a unique price limit for initiating the project. If the current electricity price is below this limit it is never optimal to invest, but above this limit investment is made according to the function for optimal size. The connection between the real option and the physical properties of a small hydropower plant is dealt with using a spreadsheet model that performs a technical simulation of the production in a plant, based on all the important choices for such a plant. The main results of the spreadsheet are simulated production size and the investment costs, which are in turn used for finding the value of the real option and the price limit. The method is illustrated on three different Norwegian small hydropower projects.     

不确定需求下的企业最优外汇持有量模型研究

把外汇作为存货看待,考虑了外汇的持有成本、转换成本、汇率风险,外汇存款利率以及利息税率等因素,通过建立数学模型来研究不确定需求下的企业最优外汇持有量问题.     

Hybrid or electric vehicles? A real options perspective

This paper investigates the decision of an automaker concerning the alternative promotion of a hybrid vehicle (HV) and a full electric vehicle (EV). We evaluate the HV project by considering the option to change promotion from the HV to the EV in the future. The results not only extend previous findings concerning American options on multiple assets, but also include several new implications. One notable observation is that increased market demand for EVs can accelerate the promotion of the HV because of the embedded option.     

High-order computational methods for option valuation under multifactor models

Many of the different numerical techniques in the partial differential equations framework for solving option pricing problems have employed only standard second-order discretization schemes. A higher-order discretization has the advantage of producing low size matrix systems for computing sufficiently accurate option prices and this paper proposes new computational schemes yielding high-order convergence rates for the solution of multi-factor option problems. These new schemes employ Galerkin finite element discretizations with quadratic basis functions for the approximation of the spatial derivatives in the pricing equations for stochastic volatility and two-asset option problems and time integration of the resulting semi-discrete systems requires the computation of a single matrix exponential. The computations indicate that this combination of high-order finite elements and exponential time integration leads to efficient algorithms for multi-factor problems. Highly accurate European prices are obtained with relatively coarse meshes and high-order convergence rates are also observed for options with the American early exercise feature. Various numerical examples are provided for illustrating the accuracy of the option prices for Heston’s and Bates stochastic volatility models and for two-asset problems under Merton’s jump-diffusion model.     

Discrete Malliavin calculus and computations of greeks in the binomial tree

This paper proposes new methods for computation of greeks using the binomial tree and the discrete Malliavin calculus. In the last decade, the Malliavin calculus has come to be considered as one of the main tools in financial mathematics. It is particularly important in the computation of greeks using Monte Carlo simulations. In previous studies, greeks were usually represented by expectation formulas that are derived from the Malliavin calculus and these expectations are computed using Monte Carlo simulations. On the other hand, the binomial tree approach can also be used to compute these expectations. In this article, we employ the discrete Malliavin calculus to obtain expectation formulas for greeks by the binomial tree method. All the results are obtained in an elementary manner.     

A Simple Derivation of and Improvements to Jamshidian's and Rogers' Upper Bound Methods for Bermudan Options

The additive method for upper bounds for Bermudan options is rephrased in terms of buyer's and seller's prices. It is shown how to deduce Jamshidian's upper bound result in a simple fashion from the additive method, including the case of possibly zero final pay‐off. Both methods are improved by ruling out exercise at sub‐optimal points. It is also shown that it is possible to use sub‐Monte Carlo simulations to estimate the value of the hedging portfolio at intermediate points in the Jamshidian method without jeopardizing its status as upper bound.