Pricing and Hedging Strategy for Options with Default and Liquidity Risk

I-Ming Jiang ； Yu-Hong Liu ； Zhi-Yuan Feng ； Meng-Kun Lai

《Asia Pacific Management Review》 17卷2期 (2012/06) Pp. 127-144

https://doi.org/10.6126/APMR.2012.17.2.02

並列摘要

This study applies fuzzy set theory to the vulnerable Black-Scholes (1973) or Merton (1973) formula. Expectations of heterogeneity mean option prices are expected to be imprecise, thus making it natural to consider fuzziness to handle this. This article presents a fuzzy approach to value Black-Scholes options subject to non-identical rationality and correlated credit risk. Although no analytical solution is available, this study employs a fuzzy approach to derive an approximate analytical expression for the upper and lower bounds of the European fuzzy vulnerable option price. Furthermore, the Greeks and hedging strategy of the proposed model are also provided in this article.

並列關鍵字

Fuzzy measure theory ； vulnerable option ； liquidity risk ； credit risk ； non-identical rationality

參考文獻

Kahneman, Daniel(ed.)Slovic, Paul(ed.),Tversky, Amos(ed.)(1982).Judgement under Uncertainty: Heuristics and Biases.UK:Cambridge University Press.

Barber, B. M.,Odean, T.(2002).Online investors: Do the slow die first?.Review of Financial Studies.15(2),455-488.

Bellman, R. E.,Zadeh, L. A.(1970).Decision-making in a fuzzy environment.Management Science.17(4),141-164.

Black, F.,Scholes, M.(1973).The valuation of options and corporate liabilities.Journal of Political Economy.81(3),637-654.

Brenner, L. A.,Koehler, D. J.,Liberman, V.,Tversky, A.(1996).Overconfidence in probability and frequency judgments.Organizational Behavior and Human Decision Processes.65(3),212-219.