Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Perspectives in supply chain risk management

1 Introduction 2 The Binomial Model 3 A More General One Period Model 4 Stochastic Integrals 5 Differential Equations 6 Portfolio Dynamics 7 Arbitrage Pricing 8 Completeness and Hedging 9 Parity Relations and Delta Hedging 10 The Martingale Approach to Arbitrage Theory (For advanced readers) 11 The Mathematics of the Martingale Approach (For advanced readers) 12 Black-Scholes from a Martingale Point of View (For advanced readers) 13 Multidimensional Models: Classical Approach 14 Multidimensional Approach: Martingale Approach (For advanced readers) 15 Incomplete Markets 16 Dividends 17 Currency Derivatives 18 Barrier Options 19 Stochastic Optimal Control 20 Bonds and Interest Rates 21 Short Rate Models 22 Martingale Models for the Short Rate 23 Forward Rate Models 24 Change of Numeraire (For advanced readers) 25 LIBOR and Swap Market Models 26 Forwards and Futures Appendix A Measure and Integration (For advanced readers) Appendix B Probability Theory (For advanced readers) Appendix C Martingales and Stopping Times (For advanced readers) References Index

http://www.gbv.de/dms/hebis-mainz/toc/071897542.pdf

Arbitrage Theory in Continuous Time

A survey of maintenance policies of deteriorating systems

While Stochastic Dominance has been employed in various forms as early as 1932, it has only been since 1969-1970 that the notion has been developed and extensively employed in the area of economics, finance, agriculture, statistics, marketing and operations research.

In this survey, the first-, second-and third-order stochastic dominance rules are discussed with an emphasis on the development in the area since the 1980s.

Stochastic dominance and expected utility: survey and analysis

We study the effects of disruption risk in a supply chain where one retailer deals with competing risky suppliers who may default during their production lead times. The suppliers, who compete for business with the retailer by setting wholesale prices, are leaders in a Stackelberg game with the retailer. The retailer, facing uncertain future demand, chooses order quantities while weighing the benefits of procuring from the cheapest supplier against the advantages of order diversification. For the model with two suppliers, we show that low supplier default correlations dampen competition among the suppliers, increasing the equilibrium wholesale prices. Therefore the retailer prefers suppliers with highly correlated default events, despite the loss of diversification benefits. In contrast, the suppliers and the channel prefer defaults that are negatively correlated. However, as the number of suppliers increases, our model predicts that the retailer may be able to take advantage of both competition and diversification.

Competition and Diversification Effects in Supply Chains with Supplier Default Risk

In this paper, we develop an efficient lattice algorithm to price European and American options under discrete time GARCH processes. We show that this algorithm is easily extended to price options under generalized GARCH processes, with many of the existing stochastic volatility bivariate diffusion models appearing as limiting cases. We establish one unifying algorithm that can price options under almost all existing GARCH specifications as well as under a large family of bivariate diffusions in which volatility follows its own, perhaps correlated, process. THROUGH AN EQUILIBRIUM ARGUMENT Duan (1995) shows that options can be priced when the dynamics for the price of the underlying instrument follows a General Autoregressive Conditionally Heteroskedastic (GARCH) process. The theory of pricing under such processes is now well understood; however, the design of efficient numerical procedures for pricing them is lacking. Most applications resort to large sample simulation methods with a variety of variance reduction techniques. The complexity of pricing arises from the massive path dependence inherent in GARCH models. This path dependence causes typical lattice-based procedures to grow exponentially in the number of time increments. The lack of efficient numerical schemes hinders empirical tests among the wide array of competing GARCH models. Most tests of GARCH models limit themselves to the use of high frequency data on spot assets, with little attention placed on the information content of options.1

Pricing Options under Generalized GARCH and Stochastic Volatility Processes

Contingent claims whose values depend on multiple sources of uncertainty arise in many financial contracts and in the analysis of real projects Unfortunately closed form solutions for these options are rare and numerical methods can be computationally expensive This article extends the literature on multinomial approximating models Specifically, new multinomial models are presented that include as special cases existing models The more general models are shown to be computationally more efficient

Multinomial Approximating Models for Options with k State Variables

For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This article identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a two-dimensional state variable Markov process. the permissible set of volatility structures that accomplishes this goal is shown to be quite large and includes many stochastic structures. In general, analytical characterization of the terminal distributions of the two state variables is unlikely, and numerical procedures are required to value claims. Efficient simulation algorithms using control variates are developed to price claims against the term structure.

/pdf/volatility-structures-of-forward-rates-and-the-dynamics-of-4me1fego3y.pdf

Volatility structures of forward rates and the dynamics of the term structure1

B oyle and Lau (hereafter BL) [1994] have illustrated how a naive application of the binomial option pricing algorithm can lead to significantly biased estimates in the prices of a variety of barrier, capped, and vulnerable options, even when the number of time steps is large. The source of the problem arises from the location of the barrier with respect to adjacent layers of nodes in the lattice. BL show that if the layers of the lattice are set up so that the barrier falls between layers of the lattice, the errors may be quite significant. To avoid these errors, they constrain the time partition so that the resulting lattice has layers that are as close as possible to the barrier. While this procedure reduces the size of errors, refining the partition size may not necessarily produce more precise results. Moreover, the BL procedure may be difficult to implement if the barriers are time-varying or if there are multiple barriers. This article provides a simple and highly efficient algorithm that can be used to price and hedge options that have single barriers that are either at constant levels or time-varying as well as contracts that are subject to multiple barriers. First, a lattice is constructed to pass through the barrier points exactly. Second, the stock price partition and the

Peter H. Ritchken

Papers

Competition and Diversification Effects in Supply Chains with Supplier Default Risk

Pricing Options under Generalized GARCH and Stochastic Volatility Processes

Multinomial Approximating Models for Options with k State Variables

Volatility structures of forward rates and the dynamics of the term structure1

On Pricing Barrier Options