Optimal Design of Multi-Asset Options

Abstract

The combination of stochastic derivative pricing models and downside risk measures often leads to the paradox (risk, return) = (−infinity, +infinity) in a portfolio choice problem. The construction of a portfolio of derivatives with high expected returns and very negative downside risk (henceforth “golden strategy”) has only been studied if all the involved derivatives have the same underlying asset. This paper also considers multi-asset derivatives, gives practical methods to build multi-asset golden strategies for both the expected shortfall and the expectile risk measure, and shows that the use of multi-asset options makes the performance of the obtained golden strategy more efficient. Practical rules are given under the Black–Scholes–Merton multi-dimensional pricing model.

Keywords

• multi-asset derivative
• downside risk measure
• unbounded market price of risk
• golden strategy