Hedging options under transaction costs and stochastic volatility

Journal of Economic Dynamics and Control

Volumn 27, Issue 6, 2003, Pages 1045-1068

  Gondzio, Jacek ^a   Kouwenberg, Roy ^b   Vorst, Ton ^b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b ERASMUS UNIVERSITY ROTTERDAM   (Netherlands)

Author keywords

Computational finance; High performance computing; Option hedging; Stochastic programming; Stochastic volatility

Indexed keywords

EID: 0037384682     PISSN: 01651889     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-1889(02)00054-4     Document Type: Article

References (37)

1. Avellaneda, M., Paras, A., 1996. Managing the volatility risk of portfolios of derivative securities: the lagrangian uncertain volatility model. Applied Mathematical Finance 3, 21-52.
2. Avellaneda, M., Levy, A., Paras, A., 1995. Pricing and hedging derivative securities in markets with uncertain volatilities. Applied Mathematical Finance 2, 73-88.
3. Bakshi, G., Cao, C., Chen, Z., 1997. Empirical performance of alternative option pricing models. Journal of Finance 52, 2003-2049.
4. Benders, J.F., 1962. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238-252.
5. Birge, J.R., Louveaux, F., 1997. Introduction to Stochastic Programming. Springer, New York.
6. Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637-659.
7. Bollerslev, T., 1986. Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 31, 307-327.
8. Bollerslev, T., Chou, R.Y., Kroner, K.F., 1992. ARCH modelling in finance: a review of the theory and empirical evidence. Journal of Econometrics 52, 55-59.
9. Boyle, P.P., Vorst, T., 1992. Option replication in discrete time with transaction costs. Journal of Finance 47, 271-291.
10. Carr, P., Ellis, K., Gupta, V., 1998. Static hedging of exotic options. Journal of Finance 53, 1165-1190.
11. Dantzig, G.B., Wolfe, P., 1961. The decomposition algorithm for linear programming. Econometrica 29, 767-778.
12. Derman, E., Ergener, D., Kani, I., 1995. Static options replication. Journal of Derivatives 2, 78-95.
13. Duan, J.-C., 1995. The GARCH option pricing model. Mathematical Finance 5, 13-32.
14. Duan, J.-C., 1997. Augmented GARCH(p,q) process and its diffusion limit. Journal of Econometrics 79, 97-127.
15. Edirisinghe, C., Naik, V., Uppal, R., 1993. Optimal replication of options with transaction costs and trading restrictions. Journal of Financial and Quantitative Analysis 28, 117-139.
16. Engle, R.F., 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 987-1008.
17. Engle, R.F., Ng, V., 1993. Measuring and testing the impact of news and volatility. Journal of Finance 48, 1749-1779.
18. Finucane, T.J., Tomas, M., 1997. American stochastic volatility call option pricing: a lattice based approach Review of Derivatives Research 1, 183-201.
19. Frey, R., Sin, C.A., 1999. Bounds on European option prices under stochastic volatility. Mathematical Finance 9, 97-116.
20. Gondzio, J., 1995. HOPDM (version 2.12) - a fast LP solver based on a primal-dual interior point method. European Journal of Operational Research 85, 221-225.
21. Gondzio, J., Kouwenberg, R., 2001. High performance computing for asset liability management. Operations Research 49 (6), 879-889.
22. Gondzio, J., Sarkissian, R., 1996. Column generation with a primal-dual method. Logilab Technical Report 96.6. University of Geneva, Switzerland.
23. Harrison, J.M., Kreps, D.M., 1 979. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20, 381-408.
24. Heston, S.L., 1993. A closed-form solution for options with stochastic volatility. Review of Financial Studies 6, 327-344.
25. Heston, S.L., Nandi, S., 1997. A closed-form GARCH option pricing model. Working Paper 97-9, Federal Reserve Bank of Atlanta.
26. Heston, S.L., Nandi, S., 1998. Preference-free option pricing with path-dependent volatility: a closed-form approach. Working Paper 98-20, Federal Reserve Bank of Atlanta.
27. Hull, J., White, A., 1987. The pricing of options on assets with stochastic volatilities. Journal of Finance 42, 218-300.
28. Klaassen, P., 1997. Discretized reality and spurious profits in stochastic programming models for asset/liability management. European Journal of Operational Research 101, 374-392.
29. Leland, H.E., 1985. Option pricing and replication with transaction costs. Journal of Finance 40, 1283-1301.
30. Naik, V., 1995. Finite state securities market models and arbitrage. In: Jarrow, R., Migdalas, A., Pardalos, P., Storøy, S.(Eds.), Handbooks in OR&MS, Vol.9. Elsevier, Amsterdam, pp. 31-64.
31. Nelson, 1990. ARCH models as diffusion approximations. Journal of Econometrics 45, 7-38.
32. Ritchken, P., Trevor, R., 1999. Pricing options under generalized GARCH and stochastic volatility processes. Journal of Finance 54, 377-402.
33. Schweizer, M., 1991. Option hedging for semimartingales. Stochastic Processes and their Applications 37, 339-363.
34. Schweizer, M., 1995. Variance-optimal hedging in discrete time. Mathematics of Operations Research 20, 1-32.
35. Scott, L., 1987. Option pricing when the variance changes randomly: theory, estimation and an application Journal of Financial and Quantitative Analysis 22, 419-438.
36. Vladimirou, H., Zenios, S.A., 1997. Parallel algorithms for large-scale stochastic programming. In: Migdals, S., Pardalos, P., Storøy, S. (Eds.), Parallel Computing in Optimization. Kluwer Academic Publishers, Amsterdam, pp. 413-469.
37. Wiggins, J., 1987. Option values under stochastic volatility: theory and empirical evidence. Journal of Financial Economics 19, 351-372.