On the Investment-Uncertainty Relationship in a Real Option Model with Stochastic Volatility

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

doi:10.2139/ssrn.1846396

Cited by 4 publications

(3 citation statements)

References 28 publications

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“…Numerous researchers have realized the deficiency of the constant volatility assumption. For example, in addition to determining 22% as a suitable annualized volatility value, Smit performs a calculation with annualized volatility values of 15% and 30% as a reference [7]. However, Smit's method is problematic when used in practice because it is very difficult for a mining company to predict the future value of the volatility of the price of mineral products.…”

Section: Convenience Yieldmentioning

confidence: 99%

“…However, some researchers believe that the use of constant volatility will result in overestimation or underestimation of the price of a mining concession because volatility can experience relatively significant variations from year to year. Therefore, it is more reasonable to assume that the volatility is stochastic (e.g., Ting et al [7] and Huang et al [8]). However, models based on this assumption are relatively complex and therefore have rarely been used in practice.…”

Section: Introductionmentioning

confidence: 99%

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Pricing Mining Concessions Based on Combined Multinomial Pricing Model

Xiao¹,

Zhang²

2017

Discrete Dynamics in Nature and Society

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A combined multinomial pricing model is proposed for pricing mining concession in which the annualized volatility of the price of mineral products follows a multinomial distribution. First, a combined multinomial pricing model is proposed which consists of binomial pricing models calculated according to different volatility values. Second, a method is provided to calculate the annualized volatility and the distribution. Third, the value of convenience yields is calculated based on the relationship between the futures price and the spot price. The notion of convenience yields is used to adjust our model as well. Based on an empirical study of a Chinese copper mine concession, we verify that our model is easy to use and better than the model with constant volatility when considering the changing annualized volatility of the price of the mineral product.

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Section: Convenience Yieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pricing Mining Concessions Based on Combined Multinomial Pricing Model

Xiao¹,

Zhang²

2017

Discrete Dynamics in Nature and Society

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“…The current transaction cost problem can be characterized as a free-boundary problem. The fast mean-reversion asymptotics for the finite horizon free boundary problem arising from American options pricing was developed in Fouque et al [2001], and recently there has been interest in similar analysis for perpetual (infinitely-lived) American options (used as part of a real options model) in Ting et al [2013], and for a structural credit risk model in McQuade [2013]. Here, we also have an infinite horizon free-boundary problem, but it is, in addition, an eigenvalue problem.…”

Section: Papermentioning

confidence: 99%

Optimal Investment with Transaction Costs and Stochastic Volatility Part I: Infinite Horizon

Bichuch¹,

Sircar²

2017

SIAM J. Control Optim.

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Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when the cost is small. Under stochastic volatility, but with no transaction costs, the Merton problem under general utility functions can also be analyzed with asymptotic methods. Here, we look at the long-run growth rate problem when both complexities are present, using separation of time scales approximations. This leads to perturbation analysis of an eigenvalue problem. We find the first term in the asymptotic expansion in the time scale parameter, of the optimal long-term growth rate, and of the optimal strategy, for fixed small transaction costs.

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American Options Under Stochastic Volatility: Control Variates, Maturity Randomization & Multiscale Asymptotics

2014

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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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On the Investment-Uncertainty Relationship in a Real Option Model with Stochastic Volatility

Cited by 4 publications

References 28 publications

Pricing Mining Concessions Based on Combined Multinomial Pricing Model

Pricing Mining Concessions Based on Combined Multinomial Pricing Model

Optimal Investment with Transaction Costs and Stochastic Volatility Part I: Infinite Horizon

American Options Under Stochastic Volatility: Control Variates, Maturity Randomization & Multiscale Asymptotics

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