2011/08/02 by Nikolai Dokuchaev, Dokuchaev, Nikolai
Economics, Econometrics and Finance · Mathematics · #91G20 #Computational Finance (q-fin.CP) #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:91G20 #q-fin.CP #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1108.0719
openalex publication_date 2011/08/02 · arxiv created 2014/09/30 · arxiv updated 2014/10/01 · openalex created_date 2022/03/02 · openalex updated_date 2026/07/28
This papers 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. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the numéraire process causes significant changes in the market properties. In particular, an equivalent martingale measure is not unique for this market, and there are non-replicable claims. The martingale prices and the hedging error can vary significantly and take extreme values, for some extreme choices of the equivalent martingale measures. Some rational choices of the equivalent martingale measures are suggested and discussed, including implied measures calculated from observed bond prices. This allows to calculate the implied market price of risk process.