The Journal of Finance

On Option Pricing Bounds

Published: 09/01/1985   |   DOI: 10.1111/j.1540-6261.1985.tb02373.x

PETER H. RITCHKEN

The purpose of this article is to compare the Perrakis and Ryan bounds of option prices in a single‐period model with option bounds derived using linear programming. It is shown that the upper bounds are identical but that the lower bounds are different. A comparison of these bounds, together with Merton's bounds and the Black‐Scholes prices in a lognormal securities market, is presented.

On Arbitrage‐Free Pricing of Interest Rate Contingent Claims

Published: 03/01/1990   |   DOI: 10.1111/j.1540-6261.1990.tb05091.x

PETER RITCHKEN, KIEKIE BOENAWAN

Unlike most interest rate claim models, the Ho‐Lee model utilizes full information on the current term structure. Unfortunately, the model has a major deficiency in that negative interest rates can occur. This article modifies the model such that interest rates are well behaved.

Pricing Options under Generalized GARCH and Stochastic Volatility Processes

Published: 05/06/2003   |   DOI: 10.1111/0022-1082.00109

Peter Ritchken, Rob Trevor

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.

Option Bounds with Finite Revision Opportunities

Published: 06/01/1988   |   DOI: 10.1111/j.1540-6261.1988.tb03940.x

PETER H. RITCHKEN, SHYANJAW KUO

This article generalizes the single‐period linear‐programming bounds on option prices by allowing for a finite number of revision opportunities. It is shown that, in an incomplete market, the bounds on option prices can be derived using a modified binomial option‐pricing model. Tighter bounds are developed under more restrictive assumptions on probabilities and risk aversion. For this case the upper bounds are shown to coincide with the upper bounds derived by Perrakis, while the lower bounds are shown to be tighter.

Lattice Models for Pricing American Interest Rate Claims

Published: 06/01/1995   |   DOI: 10.1111/j.1540-6261.1995.tb04802.x

ANLONG LI, PETER RITCHKEN, L. SANKARASUBRAMANIAN

This article establishes efficient lattice algorithms for pricing American interest‐sensitive claims in the Heath, Jarrow, and Morton paradigm, under the assumption that the volatility structure of forward rates is restricted to a class that permits a Markovian representation of the term structure. The class of volatilities that permits this representation is quite large and imposes no severe restrictions on the structure for the spot rate volatility. The algorithm exploits the Markovian property of the term structure and permits the efficient computation of all types of interest rate claims. Specific examples are provided.

Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets

Published: 09/11/2003   |   DOI: 10.1111/1540-6261.00603

Rong Fan, Anurag Gupta, Peter Ritchken

This paper examines whether higher order multifactor models, with state variables linked solely to underlying LIBOR‐swap rates, are by themselves capable of explaining and hedging interest rate derivatives, or whether models explicitly exhibiting features such as unspanned stochastic volatility are necessary. Our research shows that swaptions and even swaption straddles can be well hedged with LIBOR bonds alone. We examine the potential benefits of looking outside the LIBOR market for factors that might impact swaption prices without impacting swap rates, and find them to be minor, indicating that the swaption market is well integrated with the LIBOR‐swap market.