TITLE:
Assessing the Risks of Trading Strategies Using Acceptability Indices
AUTHORS:
Masimba E. Sonono, Hopolang P. Mashele
KEYWORDS:
Conic Finance; Coherent Risk Measure; Acceptability Indices; Incomplete Markets; Bid-Ask Prices; Continuous Time Models
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.3 No.4,
November
27,
2013
ABSTRACT: The paper looks at the quantification of risks of trading strategies in incomplete markets. We realized that the no-arbitrage price intervals are unacceptably large. From a risk management point of view, we are concerned with finding prices that are acceptable to the market. The acceptability of the prices is assessed by risk measures. Plausible risk measures give price bounds that are suitable for use as bid-ask prices. Furthermore, the risk measures should be able to compensate for the unhedgeable risk to an extent. Conic finance provides plausible bid-ask prices that are determined by the probability distribution of the cash flows only. We apply the theory to obtain bid-ask prices in the assessment of the risks of trading strategies. We analyze two popular trading strategies—bull call the spread strategy and bear call spread strategy. Comparison of risk profiles for the strategies is done between the Variance Gamma Scalable Self Decomposable model and the Black-Scholes model. The findings indicate that using bid-ask prices compensates for the unhedgeable risk and reduces the spread between bid-ask prices.