Assessing the Risks of Trading Strategies Using Acceptability Indices
- 1 Unit for Business Mathematics and Informatics, North-West University, Potchefstroom, South Africa
- 2 Centre for Business Mathematics and Informatics, North-West University, Potchefstroom, South Africa
Abstract
The paper looks at the quantification of risks of trading strategies in incomplete markets. We realized that the no-arb i trage 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 un hedge able 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.
- P. Artzner, F. Delbaen, J. Eber and D. Heath, “Definition of Coherent Measure of Risk,” Mathematical Finance, Vol. 9, No. 3, 1999, pp. 203-228. http://dx.doi.org/10.1111/1467-9965.00068
- A. Cherny and D. Madan, “New Measure of Performance Evaluation,” Review of Financial Studies, Vol. 22, No. 7, 2009, pp. 2571-2606. http://dx.doi.org/10.1093/rfs/hhn081
- J. N. Cochrane and J. Saá-Requejo, “Beyond Arbitrage: ‘Good Deal’ Asset Price Bounds in Incomplete Markets,” Journal of Political Economy, Vol. 108, No. 1, 2000, pp. 79-11. http://dx.doi.org/10.1086/262112
- J. Staum, “Incomplete Markets,” In: J. R. Birge and V. Linetsky, Handbook in Operations Research and Management Science, Vol. 15, Chapter 12, Elsevier, Berlin, 2008, pp. 511-563.
- S. Jaschke and K. Küchler, “Coherent Risk Measures and Good Deal Bounds,” Finance and Stochastics, Vol. 5, No. 2, 2001, pp. 181-200. http://dx.doi.org/10.1007/PL00013530
- A. Cherny and D. Madan, “Markets as a Counterparty: An Introduction to Conic Finance,” International Journal of Theoretical and Applied Finance, Vol. 13, No. 8, 2010, pp. 1149-1177. http://dx.doi.org/10.1142/S0219024910006157
- D. Madan, P. Carr and E. Chang, “The Variance Gamma Process and Option Pricing,” European Finance Review, Vol. 2, No. 1, 1998, pp. 79-105. http://dx.doi.org/10.1023/A:1009703431535
- P. Carr, H. Geman, D. Madan, and M. Yor, “Self Decomposability and Option Pricing,” Mathematical Finance, Vol. 17, No. 1, 2007, pp. 31-57. http://dx.doi.org/10.1111/j.1467-9965.2007.00293.x
- K. Sato, “Self Similar Processes with Independent Increments,” Probability Theory and Related Fields, Vol. 89, No. 3, 1991, pp. 285-300. http://dx.doi.org/10.1007/BF01198788
- K. Sato, “Lévy Processes and Infinitely Divisible Distributions,” Cambridge University, Cambridge, 1999.
- P. Carr, H. Geman, D. Madan and M. Yor, “Pricing Options on Realized Variance,” Finance and Stochastics, Vol. 9, No. 4, 2005, pp. 453-475. http://dx.doi.org/10.1007/s00780-005-0155-x