References
- Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. J. Polit. Econ. 81(3):637–654. doi:10.1086/260062.
- Merton, R. C. (1973). Theory of rational option pricing. Bell J. Econ. Manage. Sci. 4(1):141. doi:10.2307/3003143.
- Ingersoll, J. E. (1987). Theory of Financial Decision Making. Lanham, MD: Rowman and Littlefield.
- Fouque, J.-P., Han, C.-H. (2003). Pricing Asian options with stochastic volatility. Quant. Finan. 3(5):353–362. doi:10.1088/1469-7688/3/5/301.
- Večeř, J., Xu, M. (2004). Pricing Asian options in a semimartingale model. Quant. Finan. 4(2):170–175. doi:10.1088/1469-7688/4/2/006.
- Wang, Z., Wang, L., Wang, D.-S., Jin, Y. (2014). Optimal system, symmetry reductions and new closed form solutions for the geometric average Asian options. Appl. Math. Comput. 226:598–605. doi:10.1016/j.amc.2013.10.021.
- Bayraktar, E., Xing, H. (2011). Pricing Asian options for jump diffusion. Math. Finan. 21(1):117–143. doi:10.1111/j.1467-9965.2010.00426.x.
- Zhang, B., Oosterlee, C. W. (2013). Efficient pricing of European-style Asian options under exponential Lévy processes based on Fourier cosine expansions. SIAM J. Finan. Math. 4(1):399–426. doi:10.1137/110853339.
- Kirkby, J. L. (2016). An efficient transform method for Asian option pricing. SIAM J. Finan. Math. 7(1):845–892. doi:10.1137/16M1057127.
- Cai, N., Song, Y., Kou, S. (2015). A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3):540–554. doi:10.1287/opre.2015.1385.
- Sengupta, I. (2014). Pricing Asian options in financial markets using mellin transforms. Electr. J. Differ. Equat. 2014(234):1–9.
- Chandra, S., Mukherjee, D., Sengupta, I. (2015). PIDE and solution related to pricing of Lévy driven arithmetic type floating Asian options. Stoch. Anal. Appl. 33(4):630–652.
- Patel, K. S., Mehra, M. (2018). A numerical study of Asian option with high-order compact finite difference scheme. J. Appl. Math. Comput. 57(1-2):467–491. doi:10.1007/s12190-017-1115-2.
- Boyle, P., Draviam, T. (2007). Pricing exotic options under regime switching. Insur. Math. Econom. 40(2):267–282. doi:10.1016/j.insmatheco.2006.05.001.
- Goswami, A., Mukherjee, K. N., Patalwala, I. H., Sanjay, N. S. (2022). Regime recovery using implied volatility in Markov modulated market model. Appl. Stoch. Models Bus. Ind. 38(6):1127–1143. doi:10.1002/asmb.2719.
- Kirkby, J. L., Nguyen, D. (2020). Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models. Ann Finan. 16(3):307–351.
- Ghosh, M. K., Goswami, A. (2009). Risk minimizing option pricing in a semi-Markov modulated market. SIAM J. Control Optim. 48(3):1519–1541. doi:10.1137/080716839.
- Goswami, A., Patel, J., Shevgaonkar, P. (2016). A system of non-local parabolic PDE and application to option pricing. Stoch. Anal. Appl. 34(5):893–905.
- Goswami, A., Nandan, S. (2016). Convergence of estimated option price in a regime switching market. Indian J. Pure Appl. Math. 47(2):169–182. doi:10.1007/s13226-016-0182-7.
- Biswas, A., Goswami, A., Overbeck, L. (2018). Option pricing in a regime switching stochastic volatility model. Stat. Probab. Lett. 138:116–126. doi:10.1016/j.spl.2018.02.056.
- Milan Kumar Das, A., Goswami, S., Rajani. (2023). Inference of binary regime models with jump discontinuities. Sankhya B. 85(1):1.
- Föllmer, H., M. Schweizer (1989). Hedging of contingent claims under incomplete information. In Applied Stochastic Analysis, Vol. 5. London; New York: Gordon and Breach, p. 389–414.
- Çi̇nlar E. (2011). Graduate Texts in Mathematics. New York: Springer. Indian J. Pure Appl. Math. 47(2):169–182. doi:10.1007/978-0-387-87859-1ProbabilityandStochastics
- Goswami, A., Saha, S., Yadav, R. K. (2023). Representation of a lass of semi-Markov dynamics. J. Theor. Probab. 2023. doi:10.1007/s10959-023-01259-4.
- Matsumoto, H., Yor, M. (2005). Exponential functionals of Brownian motion. I. Probability laws at fixed time. Probab. Surv. 2:312–347.
- Pazy, A., (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, New York, NY: Springer.
- Hugger, J. (2006). Wellposedness of the boundary value formulation of a fixed strike Asian option. J. Comput. Appl. Math. 185(2):460–481. doi:10.1016/j.cam.2005.03.022.
- Royden, H., P. Fitzpatrick (2015). Real Analysis, 4th ed. India: Pearson Education.
- Schweizer, M., (2001). A guided tour through quadratic hedging approaches. In Option pricing, interest rates and risk management, Handbook in Mathematical Finance. Cambridge University Press, p. 538–574.
- Kallianpur, G., R. L. Karandikar (2000). Introduction to Option Pricing Theory. Boston, MA: Birkhäuser Boston.
- Das, M. K., Goswami, A., Patankar, T. S. (2018). Pricing derivatives in a regime switching market with time inhomogenous volatility. Stoch. Anal. Appl. 36(4):700–725. doi:10.1080/07362994.2018.1448996.
- Föllmer, H., Protter, P., Shiryayev, A. N., Follmer, H. (1995). Quadratic covariation and an extension of Itô’s formula. Bernoulli. 1(1/2):149 doi:10.2307/3318684.
- Rogers, L. C. G., Shi, Z. (1995). The value of an Asian option. J. Appl. Probab. 32(4):1077–1088. doi:10.2307/3215221.
- Ishiyama, K. (2005). Methods for Evaluating density functions of exponential functionals represented as integrals of geometric Brownian motion. Methodol. Comput. Appl. Probab. 7(3):271–283. doi:10.1007/s11009-005-4517-9.
- Privault, N., Uy, W. I. (2013). Monte Carlo computation of the Laplace transform of exponential Brownian functionals. Methodol. Comput. Appl. Probab. 15(3):511–524. doi:10.1007/s11009-011-9261-8.