2022/05/21 by Jingwei Liu, Liu, Jingwei
Economics, Econometrics and Finance · #Capital Investment and Risk Analysis #FOS: Economics and business #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2205.10665
openalex publication_date 2022/05/21 · openalex created_date 2022/05/26 · openalex updated_date 2026/07/28
We propose a general framework of European power option pricing under two different market assumptions about extended Vasicěk interest rate process and exponential Ornstein-Uhlenbeck asset process with continuous dividend as underlying, in which the Brownian motions involved in Vasicěk interest rate and exponential Ornstein-Uhlenbeck process are time-dependent correlated in equivalent martingale measure probability space or real-world probability space respectively. We first develop European power option pricing in two types of payoffs with martingale method under the market assumption that Vasicěk interest rate and exponential Ornstein-Uhlenbeck process are correlated in equivalent martingale measure probability space. Then, we solve the European power option pricing under the market assumption that Vasicěk interest rate and exponential Ornstein-Uhlenbeck process are correlated in real-world probability by constructing a Girsannov transform to map real-world probability to risk-neutral equivalent martingale measure. Finally, the European power option pricing formulae are derived with numeraire change and T-forward measure under the above two market assumptions in a uniform theoretical framework and close formulae expression.