Real-World Pricing for a Modified Constant Elasticity of Variance Model

Abstract

This paper considers a modified constant elasticity of variance (MCEV) model. This model uses the familiar constant elasticity of variance form for the volatility of the growth optimal portfolio (GOP) in a continuous market. It leads to a GOP that follows the power of a time-transformed squared Bessel process. This paper derives analytic real-world prices for zero-coupon bonds, instantaneous forward rates and options on the GOP that are both theoretically revealing and computationally efficient. In addition, the paper examines options on exchange prices and options on zero-coupon bonds under the MCEV model. The semi-analytic prices derived for options on zero-coupon bonds can subsequently be used to price interest rate caps and floors.

Key Words:

• Benchmark approach
• real-world pricing
• growth optimal portfolio
• constant elasticity of variance
• zero-coupon bonds
• exchange prices
• interest rate caps and floors

Acknowledgement

The authors thank Hardy Hulley, David Heath and Leah Kelly for their interest in this research and constructive discussions on the subject.