Efficient Numerical Valuation of Continuous Installment Options

This paper deals with a refinement of the Laplace-Carson transform (LCT) approach to option pricing, with a special emphasis on valuing defaultable and non-callable convertible bonds (CBs), but not limited to it. What we are actually aiming at is refining the plain LCT approach to meet possibly general American derivatives. The setup is a standard Black-Scholes-Merton framework where the underlying firm value evolves according to a geometric Brownian motion. The valuation of CBs can be formulated as an optimal stopping problem, due to the possibility of voluntary conversion prior to maturity. We begin with the plain LCT approach that generates a complex solution with little prospect of further analysis. To improve this solution, we introduce the notion of premium decomposition, which separates the CB value into the associated European CB value and an early conversion premium. By the LCT approach combined with the premium decomposition, we obtain a much simpler and closed-form solution for the CB value and an optimal conversion boundary. By virtue of the simplified solution, we can easily characterize asymptotic properties of the early conversion boundary. Finally, we show that our refined LCT approach is broadly applicable to a more general class of claims with optimal stopping structure.

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Valuation of American Continuous-Installment Options Under the Constant Elasticity of Variance Model

Deng

Xue

2016

Journal of Systems Science and Information

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This article prices American-style continuous-installment options in the constant elasticity of variance (CEV) diffusion model where the volatility is a function of the stock price. We derive the semi-closed form formulas for the American continuous-installment options using Kim’s integral representation method and then obtain the closed-form solutions by approximating the optimal exercise and stopping boundaries as step functions. We demonstrate the speed-accuracy of our approach for different parameters of the CEV model. Furthermore, the effects on both option price and the optimal boundaries are discussed and the causes of underestimating or overestimating the option prices are analyzed under the classical Black-Scholes-Merton model, in particular, for the case of elasticity coefficient with numerical examples.

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Efficient Numerical Valuation of Continuous Installment Options

Cited by 4 publications

References 33 publications

Pricing American continuous-installment options under stochastic volatility model

Pricing American continuous-installment options under stochastic volatility model

A Refined Laplace-Carson Transform Approach to Valuing Convertible Bonds

Valuation of American Continuous-Installment Options Under the Constant Elasticity of Variance Model

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