No-arbitrage theorem for multi-factor uncertain stock model with floating interest rate
Tóm tắt
In the stock models, the prices of the stocks are usually described via some differential equations. So far, uncertain stock model with constant interest rate has been proposed, and a sufficient and necessary condition for it being no-arbitrage has also been derived. This paper considers the multiple risks in the interest rate market and stock market, and proposes a multi-factor uncertain stock model with floating interest rate. A no-arbitrage theorem is derived in the form of determinants, presenting a sufficient and necessary condition for the new stock model being no-arbitrage. In addition, a strategy for the arbitrage is provided when the condition is not satisfied.
Tài liệu tham khảo
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.
Chen, X. (2011). American option pricing formula for uncertain financial market. International Journal of Operations Research, 8(2), 32–37.
Chen, X., Liu, Y., & Ralescu, D. A. (2013). Uncertain stock model with periodic dividends. Fuzzy Optimization and Decision Making, 12(1), 111–123.
Chen, X., & Gao, J. (2013). Uncertain term structure model of interest rate. Soft Computing, 17(4), 597–604.
Galai, D., & Masulis, R. W. (1976). The option pricing model and the risk factor of stock. Journal of Financial Economics, 3(1), 53–81.
Guerard, J. B., Markowitz, H., & Xu, G. (2015). Earnings forecasting in a global stock selection model and efficient portfolio construction and management. International Journal of Forecasting, 31(2), 550–560.
Ji, X., & Zhou, J. (2015). Option pricing for an uncertain stock model with jumps. Soft Computing, 19(11), 3323–3329.
Jiao, D., & Yao, K. (2015). An interest rate model in uncertain environment. Soft Computing, 19(3), 775–780.
Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin Heidelberg: Springer.
Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16.
Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin Heidelberg: Springer.
Liu, B. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications, 1(1), 1–15.
Peng, J., & Yao, K. (2011). A new option pricing model for stocks in uncertainty markets. International Journal of Operations Research, 8(2), 18–26.
Samuelson, P. A. (1965). Rational theory of warrant pricing. Industrial Management Review, 6(2), 13–31.
Thavaneswaran, A., Appadoo, S. S., & Frank, J. (2013). Binary option pricing using fuzzy numbers. Applied Mathematics Letters, 26(1), 65–72.
Wu, H. C. (2004). Pricing European options based on the fuzzy pattern of Black-Scholes formula. Computers and Operations Research, 31(7), 1069–1081.
Wu, H. C. (2005). European option pricing under fuzzy environments. International Journal of Intelligent Systems, 20(1), 89–102.
Wu, H. C. (2007). Using fuzzy sets theory and Black-Scholes formula to generate pricing boundaries of European options. Applied Mathematics and Computation, 185(1), 136–146.
Yao, K. (2015). A no-arbitrage theorem for uncertain stock model. Fuzzy Optimization and Decision Making, 14(2), 227–242.
Yao, K. (2015). Uncertain contour process and its application in stock model with floating interest rate. Fuzzy Optimization and Decision Making, 14(4), 399–424.
Yoshida, Y. (2003). The valuation of European options in uncertain environment. European Journal of Operational Research, 145(1), 221–229.
Yu, X. (2012). A stock model with jumps for uncertain markets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 20(3), 421–432.
Zhang, Z., Ralescu, D. A., & Liu, W. (2015). Valuation of interest rate ceiling and floor in uncertain financial market. Fuzzy Optimization and Decision Making. doi:10.1007/s10700-015-9223-7.
Zhu, Y. (2015). Uncertain fractional differential equations and an interest rate model. Mathematical Methods in the Applied Sciences, 38(15), 3359–3368.