PETER RITCHKEN

Option and Forward Contracting with Asymmetric Information:

Valuation Issues in Supply Chains

H. Li, P. Ritchken and Y. Wang

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. The supplier, aware of this asymmetry, and acting as a Stackelberg leader, designs contracting arrangements 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. We examine how individual agents' profits are affected by the contracting arrangements and by the degree of asymmetric information. Finally, we investigate how alternative contracting arrangements alters the expected value of obtaining information that eliminates asymmetric information.

 V Babich, A. Burnetas, P. Ritchken

We study the effects of credit 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 establishing 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 reducing credit risk through diversification. If the wholesale prices were exogenous, the retailer would benefit by choosing suppliers that had low default correlations. However, when prices are endogenous, low supplier default correlations dampens competition among the suppliers, increasing the equilibrium wholesale prices. We show that the retailer prefers suppliers with highly correlated default events. In contrast, the suppliers and the channel prefer defaults that are negatively correlated.

Jump Starting GARCH:Pricing and Hedging Options with Jumps in Returns and Volatilities

J. Duan, P. Ritchken, Z. Sun

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan's GARCH option models, where conditional returns are constrained to being normal, as well as mixed jump processes as used in Merton. Indeed, the diffusion limits of our model include stochastic volatility models, such as Heston, jump diffusion models where jump risk is priced, and models where there are jumps and diffusive elements in both returns and volatilities. Empirical analysis on the S&P 500 index reveals that the incorporation of jumps in returns and volatilities adds significantly to the description of the time series process. Moreover, incorporating information from panels of option prices leads to significant improvements in option pricing performance. .
We find that option prices, even 50 weeks after the parameters are estimated, are fairlyprecise. In addition to pricing tests, we examine hedging effectiveness, andprovide evidence that the hedges can be maintained very well over time.

On Correlation Effects and Systemic Risk in Credit Models

P. Ritchken and Z. Sun

We establish models where the credit spreads of multiple firms and the term structure of interest rates at any future date can be represented, analytically, in terms of a finite number of state variables. The models make no restrictions on the correlation structure between interest rates and credit spreads. Default correlations among credit spreads of different firms are induced by allowing the intensity rates of different firms to be correlated with each other. In addition, default events can impact credit spreads of surviving firms in related industries. This feature allows a greater clustering of defaults. Our multifactor models allows us to explore the effects of correlations betwen interest and credit sensitive contracts and among different credits, and to examine the effects of systemic risk.

On Pricing Derivatives in the Presence of Auxiliary State Variables

J. Lin and P. Ritchken.

This article investigates the pricing of options when a need arises to carry a path dependent auxiliary state variable. Examples of such problems include the pricing of interest rate claims in a Heath Jarrow Morton paradigm, where the underlying forward rates follow a Markovian process, and the pricing of equity options, when the underlying asset price follows a GARCH process. In the former case, the primary state variable is the spot interest rate, and the auxiliary state variable is the accrued variance of the current spot rate. In the latter case, the primary state variable is the asset price, and the auxiliary state variable is the path dependent statistic representing local volatility. An efficient algorithm is developed for pricing claims under these type of processes. Illustrative examples are presented that demonstrate the efficiency of the algorithm and conditions are developed that ensure the algorithm will produce accurate prices.

An Empirical Comparison of GARCH Option Pricing Models

K. C. Hsieh, and P. Ritchken

Heston and Nandi (2000) provide considerable empirical support for their GARCH option pricing model. Their model has the advantage that analytical solutions are available for pricing European options. This article takes a closer look at this model and compares its performance with the NGARCH option model of Duan~(1995). We confirm Heston and Nandi's findings, namely that their model can explain a significant portion of the volatility smile. However, we show that the NGARCH model is superior in removing biases from pricing residuals for all moneyness and maturity categories especially for out-the-money contracts. The out-of-sample performance of both GARCH models is closely examined, and the NGARCH model is shown to have very attractive properties. The NGARCH model continues to perform well, even when the parameters of the model are not re-estimated for long periods of time. Given the existence of relatively efficient algorithms for pricing American claims and exotics under NGARCH processes, we recommend that traders and risk managers consider the NGARCH model.

On Pricing and Hedging in the Swaption Market: How Many Factors, Really?

R. Fan, A. Gupta, P. Ritchken

This article investigates the performance of several one, two, three and four factor models of the term structure for pricing caps and swaptions. Our goal is to evaluate how the number of stochastic drivers and their associated volatility structures affect pricing. For caps, we show that incorporating level dependence and a maturity hump in the volatilities of forward rates are important features that reduce pricing biases. However, none of the models we consider are able to eliminate large and systematic out of sample pricing errors. For swaptions, however, we show that certain low dimensional one and two factor models are capable of performing as well as higher order multifactor models, in spite of the fact that they do not reflect historical correlations that exist among forward rates. Our empirical findings have strong implications for modeling and risk management of an array of actively traded derivatives that closely relate to caps and swaptions.

A Pricing Model for Credit Derivatives:

Application to Default Swaps and Credit Spreads

R. Fan and P. Ritchken

In this article we develop a three factor model for pricing risky bonds. When credit worthiness is not an issue the model collapses to a two factor Heath Jarrow Morton model where forward rate volatilities are humped functions of their maturities and discount bonds are priced at their market values. Risky forward rates are generated by an additional factor. We establish an analytical model for risky bond prices and for a term structure of credit spreads. Our model permits interest rates to be arbitrarily correlated with the short term credit spread. In addition, the credit spread is mean reverting, and, if the parameters of the process are nonnegative, the credit spreads are guaranteed to be positive. The credit spread model is capable of generating an array of credit spread curves similar to those encountered in practice. Models are also developed for a few credit derivatives including default swaps. The fair default swap rate is compared to the credit spread and the difference linked to correlation effects between interest rates and short credit spreads.