Perpetual American Options in Regime-Switching Models

Perpetual American Options in Regime-Switching Models
Author: Svetlana Boyarchenko
Publisher:
Total Pages: 27
Release: 2007
Genre:
ISBN:

In the paper, we solve the pricing problem for perpetual American options in Markov-modulated Levy models. The early exercise boundaries and prices are calculated using an iteration procedure. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modelled as finite-state Markov chains.

Pricing American Options in Regime-Switching Models

Pricing American Options in Regime-Switching Models
Author: Svetlana Boyarchenko
Publisher:
Total Pages: 0
Release: 2008
Genre:
ISBN:

The pricing problem for American options in Markov-modulated Lévy models is solved. The early exercise boundaries and prices are calculated using a generalization of Carr's randomization procedure for regime-switching models. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. In contrast with the earlier version of the method, an explicit algorithm is formulated for wide classes of Lévy processes, and FFT and iFFT are used.

American Options in Regime-Switching Models

American Options in Regime-Switching Models
Author: Svetlana Boyarchenko
Publisher:
Total Pages: 36
Release: 2007
Genre:
ISBN:

In the paper, we solve the pricing problem for American options in Markov-modulated Levy models. The early exercise boundaries and prices are calculated using a generalization of Carr's randomization for regime-switching models. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modelled as finite-state Markov chains.

Pricing American Options Under Regime Switching Using Method of Lines

Pricing American Options Under Regime Switching Using Method of Lines
Author: Carl Chiarella
Publisher:
Total Pages: 19
Release: 2016
Genre:
ISBN:

This paper considers the American option pricing problem under regime-switching by using the method-of-lines (MOL) scheme. American option prices in each regime involve prices in all other regimes. We treat the prices from other regimes implicitly, thus guaranteeing consistency. Iterative procedures are required but very few iterative steps are needed in practice. Numerical tests demonstrate the robustness, accuracy and efficiency of the proposed numerical scheme. We compare our results with Buffington and Elliott (2002)'s analytical approximation under two regimes. Our MOL scheme provides improved results especially for out-of-the money options, possibly because they use a separation of variable approach to the PDEs which cannot hold around the early exercise region. We also compare our results with those of Khaliq and Liu (2009) and suggest that their implicit scheme can be improved.

A Direct Solution Method for Pricing Options in Regime-Switching Models

A Direct Solution Method for Pricing Options in Regime-Switching Models
Author: Masahiko Egami
Publisher:
Total Pages: 28
Release: 2018
Genre:
ISBN:

Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime-switching models. In this article, we reduce an optimal stopping problem with an arbitrary value function in a two-regime environment to a pair of optimal stopping problems without regime switching. We then propose a method for finding optimal stopping rules using the techniques available for non-switching problems. In contrast to other methods, our systematic solution procedure is more direct since we first obtain the explicit form of the value functions. In the end, we discuss an option pricing problem which may not be dealt with by the conventional methods, demonstrating the simplicity of our approach.

American Options in Regime-Switching Lévy Models With Non-Semibounded Stochastic Interest Rates

American Options in Regime-Switching Lévy Models With Non-Semibounded Stochastic Interest Rates
Author: Svetlana Boyarchenko
Publisher:
Total Pages: 6
Release: 2008
Genre:
ISBN:

A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Leacute;vy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. Contrary to the earlier version of the method, the interest rate may assume non-positive values. As applications, explicit algorithms for Vasicek and Black's models with jumps are derived. Numerical examples show that the option prices in these two models are very close.

Stochastic Theory and Control

Stochastic Theory and Control
Author: Bozenna Pasik-Duncan
Publisher: Springer Science & Business Media
Total Pages: 563
Release: 2002-07-24
Genre: Mathematics
ISBN: 3540437770

This volume contains almost all of the papers that were presented at the Workshop on Stochastic Theory and Control that was held at the Univ- sity of Kansas, 18–20 October 2001. This three-day event gathered a group of leading scholars in the ?eld of stochastic theory and control to discuss leading-edge topics of stochastic control, which include risk sensitive control, adaptive control, mathematics of ?nance, estimation, identi?cation, optimal control, nonlinear ?ltering, stochastic di?erential equations, stochastic p- tial di?erential equations, and stochastic theory and its applications. The workshop provided an opportunity for many stochastic control researchers to network and discuss cutting-edge technologies and applications, teaching and future directions of stochastic control. Furthermore, the workshop focused on promoting control theory, in particular stochastic control, and it promoted collaborative initiatives in stochastic theory and control and stochastic c- trol education. The lecture on “Adaptation of Real-Time Seizure Detection Algorithm” was videotaped by the PBS. Participants of the workshop have been involved in contributing to the documentary being ?lmed by PBS which highlights the extraordinary work on “Math, Medicine and the Mind: Discovering Tre- ments for Epilepsy” that examines the e?orts of the multidisciplinary team on which several of the participants of the workshop have been working for many years to solve one of the world’s most dramatic neurological conditions. Invited high school teachers of Math and Science were among the part- ipants of this professional meeting.

Option Pricing Under Regime-Switching Models

Option Pricing Under Regime-Switching Models
Author: Frédéric Godin
Publisher:
Total Pages: 46
Release: 2018
Genre:
ISBN:

Although option pricing schemes in regime-switching frameworks were extensively explored in the literature, many models developed disregard the unobservability of regimes. In such a context, the traditional pricing approach pioneered by Hardy (2001) applied to vanilla options exhibits path-dependence even if the underlying asset price process can be embedded in a Markov process. This property is deemed counterintuitive and puzzling, warranting explanations and alternatives. The current work develops novel risk-neutral measures which remove the path-dependence issue. Pricing approaches based on dynamic programming and Monte-Carlo simulations which rely on the latter measures are illustrated.

Option Pricing Under Regime Switching (analytical, PDE, and FFT Methods)

Option Pricing Under Regime Switching (analytical, PDE, and FFT Methods)
Author: Mohammad Yousef Akhavein Sohrabi
Publisher:
Total Pages: 83
Release: 2011
Genre:
ISBN:

Although globally used in option pricing, the Black-Scholes model has not been able to reflect the evolution of stocks in the real world. A regime-switching model which allows jumps in the underlying asset prices and the parameters of the corresponding stochastic process is more accurate. We evaluate the analytical solution for pricing of European options under a two-state regime switching model. Both the convergence of the analytical solution and the feature of implied volatility are investigated through numerical examples.