Peter H. Ritchken

Competition and Diversification Effects in Supply Chains with Supplier Default Risk

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.

Pricing Options under Generalized GARCH and Stochastic Volatility Processes

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. Copyright The American Finance Association 1999.

On Pricing Barrier Options

Pricing and hedging barrier options using a binomial lattice can be quite delicate. If the barrier is not constant, or if there are multiple barriers, then in all likelihood binomial lattices will produce erroneous answers even when a large number of time steps are used. While in some cases the time partitions of the binomial method can be carefully chosen so as to reduce the bias, for many barrier contracts more efficient procedures exist. This article explains how a very simple and extremely efficient trinomial lattice procedure can be used to price and hedge most types of exotic barriers.

Option Pricing with Downward-Sloping Demand Curves: The Case of Supply Chain Options

This article investigates the role of option contracts in a supply chain when the demand curve is downward sloping. We consider call (put) options that provide the retailer with the right to reorder (return) goods at a fixed price. We show that the introduction of option contracts causes the wholesale price to increase and the volatility of the retail price to decrease. In general, options are not zero-sum games. Conditions are derived under which the manufacturer prefers to use options. When this happens the retailer is also better off, if the uncertainty in the demand curve is low. However, if the uncertainty is sufficiently high, then the introduction of option contracts alters the equilibrium prices in a way that hurts the retailer.

Contingent Claims Contracting for Purchasing Decisions in Inventory Management

Option pricing is a common and important practice in the financial community, and has become a fundamental theoretical construct in financial economics. The theory is quite rich and has potential uses in many other problem domains. This paper develops a variant of the theory as applied to inventory planning. In particular, we consider a risk management approach that uses negotiated option contracts for hedging against price and quantity uncertainty in inventory procurement. We derive conditions for the inclusion of options in inventory control as a function both of managerial attitudes toward risk and of the correlation between price and demand.

Option pricing under regime switching

Abstract This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357–84), in which volatility influences returns. In addition, our models allow for feedback effects from returns to volatilities. Our family also includes GARCH option models as a special limiting case. Our models are more general than GARCH models in that our variance updating schemes do not only depend on levels of volatility and asset innovations, but also allow for a second factor that is orthogonal to asset innovations. The underlying processes in our family capture the asymmetric response of volatility to good and bad news and thus permit negative (or positive) correlation between returns and volatility. We provide the theory for pricing options under such processes, present an analytical solution for the special case where returns provide no feedback to volatility levels, and develop an efficient algorithm for the computation of American option prices for the general case.

APPROXIMATING GARCH‐JUMP MODELS, JUMP‐DIFFUSION PROCESSES, AND OPTION PRICING

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 the limiting models for our approximating GARCH Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffusion processes with correlated jump sizes. Convergence of a few GARCH models to their continuous time limits is evaluated and the benefits of the models explored.

Option and forward contracting with asymmetric information: Valuation issues in supply chains

We investigate the role of forward commitments and option contracts between a seller (supplier) and a buyer (retailer) in the presence of asymmetric information. In our case, both parties face price and demand uncertainty but the retailer, being closer to the market, has additional information about the true demand and price. The supplier, aware of this asymmetry, and acting as a Stackelberg leader, designs a contracting arrangement that best meet his interest. We contrast the role of forward and option contracts in this environment and identify cases where combinations of the two are dominant. Finally, we investigate how alternative contracting arrangements alter the expected value of obtaining information that eliminates asymmetric information.

Contracting with Asymmetric Demand Information in Supply Chains

When a retailer holds no private information, a powerful supplier can use several contract types to extract for herself the first-best channel profit, leaving the retailer nothing but his reservation profit. In the case where the retailer holds private information on the probability distribution of market demand, most well analyzed contracts do not allow the supplier to achieve for herself the first-best channel profit. In equilibrium, the retailer is able to extract an information rent above his reservation profit, and the overall channel may deviate from its first-best solution. This paper shows that using judicially designed wholesale price contracts involving a buyback policy, a supplier can theoretically avoid paying any information rent to the privately informed retailer, and, at the same time, can extract all the first-best channel profit.

Interest Rate Option Pricing With Volatility Humps

This paper develops a simple model for pricing interest rate options when the volatility structure of forward rates is humped. Analytical solutions are developed for European claims and efficient algorithms exist for pricing American options. The interest rate claims are priced in the Heath-Jarrow-Morton paradigm, and hence incorporate full information on the term structure. The structure of volatilities is captured without using time varying parameters. As a result, the volatility structure is stationary. It is not possible to have all the above properties hold in a Heath Jarrow Morton model with a single state variable. It is shown that the full dynamics of the term structure is captured by a three state Markovian system. Caplet data is used to establish that the volatility hump is an important feature to capture.