ABSTRACT
This chapter deals with special market models including models with an unbounded appreciation rate and models with random bond prices described by Ito’s equations. It considers a so-called mean-reverting single stock market model with constant risk-free rate model, and examines its arbitrage opportunities and other speculative opportunities. Under the mean-reverting settings, the return at time t tends to reverse to the long-term average of returns, and the variance of the process is lower than for a martingale with the same volatility. The chapter addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. An equivalent martingale measure is not unique for this market, and there are non-replicable claims. The chapter describes a market model consisting of two tradable assets with random continuous in time prices representing a modification of the classical Black–Scholes model where one of the assets is non-random.
