Market Price of Risk and Random Field Driven Models of Term Structure: A Space-Time Change of Measure Look

TL;DR

This paper introduces a general space-time change of measure framework for no-arbitrage term structure models, allowing the market price of risk to depend on asset-specific characteristics, extending prior models.

Contribution

It extends existing models by allowing the market price of risk to vary with asset features using a novel space-time change of measure theorem.

Findings

Market price of risk can depend on asset characteristics.

The proposed framework generalizes previous models.

Quantitative analysis of asset-dependent risk premium.

Abstract

No-arbitrage models of term structure have the feature that the return on zero-coupon bonds is the sum of the short rate and the product of volatility and market price of risk. Well known models restrict the behavior of the market price of risk so that it is not dependent on the type of asset being modeled. We show that the models recently proposed by Goldstein and Santa-Clara and Sornette, among others, allow the market price of risk to depend on characteristics of each asset, and we quantify this dependence. A key tool in our analysis is a very general space-time change of measure theorem, proved by the first author in earlier work, and covers continuous orthogonal local martingale measures including space-time white noise.