Abstracts

Many financial institutions use various models for various purposes such as investment, risk management and pricing derivatives. Usually a model includes some parameters but it is difficult or impossible to know all true parameters perfectly. We call the risk caused by not knowing the true parameters, the model risk. In the classical theory, the model risk is neglected but it is one of the most important risks. Recently some problems in the financial world are studied with consideration for the model risk.
We are interested in a mean reverting interest rated model. A mean reverting interest rate model is suitable for practical use. We can calculate prices of complicated derivatives on interest rate by a mean reverting model. A mean reverting model can be represented by both a continuous time model and a discrete time model. These models include some parameters and then there is the model risk.
In this study, we consider a mean reverting interest rate model whose volatility process is uncertain. We consider an investor who knows the volatility process moves between two deterministic processes but he does not know the true volatility process. Most of prices of interest rate derivatives cannot be determined uniquely, based on this interest rate model. Our problem is to find the price bounds of a derivative, that is, we want to find the maximum and minimum prices. To solve the problem, we propose a trinomial model and show how to calculate the price bounds using the dynamic programming method. Our trinomial model is related with the uncertain volatility model proposed by Avellaneda, Levy and Paras (1995) and the Hull White interest rate model in Hull and White (1994, 1996). By the numerical experiments, we study the model risk of options and their portfolios. We show the optimal volatility process which attains the maximum price or the minimum price. Further we study the portfolio effect of the model risk.