Abstract
Multi-asset options are created to accelerate investment among countries with the development of globalization and financial market integration. Considering the human uncertainty and the influence of sudden events such as wars and economic crisis, this paper proposes an uncertain model of multi-asset price with uncertain jumps. Option pricing formulas for the European-style dual-strike option, product option, and quotient option are derived.
Highlights
Wiener process was used as the stock price process as early as 1900 by Bachelier
We study the uncertain jump process which consists of two parts
We propose an uncertain model of asset price which contains multiassets and uncertain jumps
Summary
Wiener process was used as the stock price process as early as 1900 by Bachelier. Since Wiener process allows negative value which is violating the reality, geometric Brownian motion with positive drift was proposed to describe the stock price by Samuelson [17]. By assuming stock price followed a geometric canonical Liu process, Liu [14] derived the European option pricing Yao [18] defined an uncertain integral with respect to uncertain renewal process and proposed a concept of uncertain differential equation with jumps.
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