American Options in Regime-Switching Models

Boyarchenko, Svetlana; Levendorskiı̌, Sergei

doi:10.2139/ssrn.929215

Cited by 20 publications

(20 citation statements)

References 26 publications

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“…Jacka and Ocejo [12] studied the regularity of the value function for a finite-horizon optimal stopping problem in the presence of regime-switching uncertainty. Boyarchenkp and Levendorski [13] calculated the early exercise boundaries for American options by using a generalization of Carr's randomization procedure for regime-switching models. In the insurance literature, Siu [14] considered the fair valuation of a participating life insurance policy with surrender options for regime-switching models and provided a decomposition result for the value of the policy.…”

Section: Introductionmentioning

confidence: 99%

Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

Luo

Xing

2021

Mathematical Problems in Engineering

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This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.

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Section: Introductionmentioning

confidence: 99%

Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

Luo

Xing

2021

Mathematical Problems in Engineering

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“…e abovementioned authors mainly concentrated on the value function and did not investigate the free boundary arising from American option pricing problem. Boyarchenkp and Levendorski calculated the early exercise boundaries for American options by using a generalization of Carr's randomization procedure for regimeswitching models [13]. But they did not study the properties of the free boundary and the early exercise premium was unknown.…”

Section: Introductionmentioning

confidence: 99%

Optimal Selling Strategies under Regime-Switching Market Environment with Finite Expiry

Xing

2021

Discrete Dynamics in Nature and Society

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This paper addresses an optimal stock liquidation problem over a finite-time horizon; to that end, we model it as an optimal stopping problem in a regime-switching market. The optimal stopping time is written as a solution to a system of Volterra type integral equations. Moreover, it reveals that when the risk-free interest rate is always lower than the return rate of the stock, it is never optimal to sell the stock early; otherwise, one should sell the stock in bear market if the stock price reaches a critical value and hold the stock in bull market until the maturity date. Finally, we present a trinomial tree method for numerical implementation. The numerical results are consistent with the theoretical findings.

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“…Such studies use numerical schemes to demonstrate the application of the results, but do not offer a universal method to find the value function explicitly. The numerical methods for the evaluation of the value function are discussed in Boyarchenko and Levendorskiǐ (), Huang, Forsyth, and Labahn (), Babbin, Forsyth, and Labahn (), as well. Another approach is to first guess a solution by constructing an optimal strategy and then prove that the candidate function is indeed a value function (e.g., see Guo & Zhang, ).…”

Section: Introductionmentioning

confidence: 99%

A direct solution method for pricing options in regime‐switching models

Egami

Kevkhishvili

2019

Mathematical Finance

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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 nonswitching problems. In contrast to other methods, our systematic solution procedure is more direct as 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.

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American Options in Regime-Switching Models

Cited by 20 publications

References 26 publications

Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

Optimal Selling Strategies under Regime-Switching Market Environment with Finite Expiry

A direct solution method for pricing options in regime‐switching models

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