On the investment–uncertainty relationship in a real option model with stochastic volatility

Ting, Sai Hung Marten; Ewald, Christian‐Oliver; Wang, Wenkai

doi:10.1016/j.mathsocsci.2013.01.005

Cited by 17 publications

(12 citation statements)

References 18 publications

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“…Ting et al [27] performed a similar analysis as in Proposition 2, but for the case of a perpetual American option i.e. λ = 0, under fast-mean reverting stochastic volatility.…”

Section: Asymptotic Analysismentioning

confidence: 99%

American options under stochastic volatility: control variates, maturity randomization & multiscale asymptotics

Agarwal

Juneja

Sircar

2015

Quantitative Finance

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American options are actively traded worldwide on exchanges, thus making their accurate and efficient pricing an important problem. As most financial markets exhibit randomly varying volatility, in this paper we introduce an approximation of American option price under stochastic volatility models. We achieve this by using the maturity randomization method known as Canadization. The volatility process is characterized by fast and slow scale fluctuating factors. In particular, we study the case of an American put with a single underlying asset and use perturbative expansion techniques to approximate its price as well as the optimal exercise boundary up to the first order. We then use the approximate optimal exercise boundary formula to price American put via Monte Carlo. We also develop efficient control variates for our simulation method using martingales resulting from the approximate price formula. A numerical study is conducted to demonstrate that the proposed method performs better than the least squares regression method popular in the financial industry, in typical settings where values of the scaling parameters are small. Further, it is empirically observed that in the regimes where scaling parameter value is equal to unity, fast and slow scale approximations are equally accurate.

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“…Ting et al [27] performed a similar analysis as in Proposition 2, but for the case of a perpetual American option i.e. λ = 0, under fast-mean reverting stochastic volatility.…”

Section: Asymptotic Analysismentioning

confidence: 99%

American options under stochastic volatility: control variates, maturity randomization & multiscale asymptotics

Agarwal

Juneja

Sircar

2015

Quantitative Finance

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“…Hsu and Lambrecht [5], and Graham [3] studied the strategic real options and the effects of private information on the investment time decisions. Recently, Ting et al [9] presented an asymptotic analysis on real options under the fast mean-reverting and the geometric mean-reverting regimes of the stochastic volatility.…”

Section: Introductionmentioning

confidence: 99%

“…The motivation of this paper is to extend the results in [9] to a competitive environment. Specifically, we use Heston's stochastic volatility model to build a duopoly real option model.…”

Section: Introductionmentioning

confidence: 99%

“…When we determine the optimal investment thresholds and the payoff of each firm, we consider both competitive and non-competitive situations. To this end, we first modify the model in [9] by adding a demand function of the market, and find that follower's optimal strategy is similar to that in the monopoly model. Then, we investigate leader's optimal strategy by determining leader's project value.…”

Section: Introductionmentioning

confidence: 99%

“…The investment-timing problem has been considered by many authors under the assumption that the instantaneous volatility of the demand shock is constant. Recently, Ting et al [9] carried out an asymptotic approach in a monopoly model by letting the volatility parameter follow a stochastic process. In this paper, we consider a strategic game in which two firms compete for a new market under an uncertain demand, and extend the analysis of Ting et al to duopoly models under different strategic game structures.…”

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confidence: 99%

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Strategic real options with stochastic volatility in a duopoly model

Huang

Cao

Chung

2014

Chaos, Solitons & Fractals

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Abstract. The investment-timing problem has been considered by many authors under the assumption that the instantaneous volatility of the demand shock is constant. Recently, Ting et al. [9] carried out an asymptotic approach in a monopoly model by letting the volatility parameter follow a stochastic process. In this paper, we consider a strategic game in which two firms compete for a new market under an uncertain demand, and extend the analysis of Ting et al. to duopoly models under different strategic game structures. In particular, we investigate how the additional uncertainty in the volatility affects the investment thresholds and payoffs of players. Several numerical examples and comparison of the results are provided to confirm our analysis.

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Staged Deployment of LEO Communication Satellite Constellation Based on Real Option Theory

Wang,

Zhang

2023

Mechanisms and Machine Science

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On the investment–uncertainty relationship in a real option model with stochastic volatility

Cited by 17 publications

References 18 publications

American options under stochastic volatility: control variates, maturity randomization & multiscale asymptotics

American options under stochastic volatility: control variates, maturity randomization & multiscale asymptotics

Strategic real options with stochastic volatility in a duopoly model

Staged Deployment of LEO Communication Satellite Constellation Based on Real Option Theory

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