Closed form spread option valuation

Bjerksund, Petter; Stensland, Gunnar

doi:10.1080/14697688.2011.617775

Cited by 58 publications

(52 citation statements)

References 7 publications

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“…Simulation may generate an accurate result, but often takes long time for computation. On the other hand, some closed form approximations are shown with good accuracy and require much less time to compute (Bjerksund and Stensland 2011). In this paper, we use the approximation in Kirk (1995), which is widely used in practice especially in energy markets (Kirk 1995) for its accuracy and simplicity.…”

Section: Modellingmentioning

confidence: 99%

Real option approach to evaluate cores for remanufacturing in service markets

Wei

Tang

2014

International Journal of Production Research

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Acquisition of cores is important for the success of remanufacturing business, but evaluating the value of cores is difficult due to many uncertain issues in the remanufacturing system. In this paper, we examine the value of cores using the real option valuation (ROV) approach, which well captures the production flexibility and represents different operations options in remanufacturing. First, in a system where the demand of remanufactured products is low, we focus on the uncertainty of price. We compare the cases where disposing cores occurs only at the expiration time and before that. The model also identifies under which circumstances disposing core early brings in more benefit. Furthermore, we study a remanufacturing system where demand and return are both uncertain. In this case, a spread option is used for evaluating the marginal value of obtaining additional cores. This approach also brings the advantage of linking the correlation between demand and return, which in fact is often exhibited in remanufacturing. The numerical experiments indicate that this correlation has an impact on collecting policies. This study illustrates the possibility of using ROV for core pricing modelling, and the study results also provide some managerial insights in managing returned cores.

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Section: Modellingmentioning

confidence: 99%

Real option approach to evaluate cores for remanufacturing in service markets

Wei

Tang

2014

International Journal of Production Research

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“…Fast prices are obtained using λ = 3 and converged price are obtained using λ = 9. The errors of the three approximation methods are also provided for reference: Bjerksund and Stensland () (BjSt Err), Lo () (Lo Err), and Li et al () (LDZ Err). Factor matrices V for ρ 12 = 90% and −90% are displayed in (b) and (c), respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In this example, the adjustment step Equation (23) is triggered for V 21 with ε ¼ 0:01. In addition, this study independently implements the analytic approximation methods of Bjerksund and Stensland (2014), Lo (2015), and Li et al (2008) for spread options. 1 All the three methods work well on S1, showing errors in the order of 10 À6 or less.…”

Section: Spread Optionsmentioning

confidence: 99%

Section: Spread Optionsmentioning

confidence: 99%

“…First, a review is conducted of the analytic methods of approximating the option price or the lower and upper bounds of the option price. For the spread option, Kirk's formula (Kirk, ) that is widely used in practice is an approximate generalization of Margrabe's formula (Margrabe, ) for an exchange option, that is, a spread option with zero‐strike price; several improvements to the formula have followed (Bjerksund & Stensland, , Lo, ). Carmona and Durrleman () computes the lower bound of a spread option price as the maximum over the prices from all possible linear, and therefore sub‐optimal, exercise boundaries.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options

Choi

2018

Journal of Futures Markets

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Contrary to the common view that exact pricing is prohibitive owing to the curse of dimensionality, this study proposes an efficient and unified method for pricing options under multivariate Black–Scholes–Merton (BSM) models, such as the basket, spread, and Asian options. The option price is expressed as a quadrature integration of analytic multi‐asset BSM prices under a single Brownian motion. Then the state space is rotated in such a way that the quadrature requires much coarser nodes than it would otherwise or low varying dimensions are reduced. The accuracy and efficiency of the method is illustrated through various numerical experiments.

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Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

Deelstra

Kozpınar

Simon

2018

Appl Stoch Models Bus & Ind

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This paper considers the evaluation of spread and basket options when the underlying asset prices are driven by Markov-modulated Lévy processes with synchronous jumps. In particular, the asset prices may jump whenever there is a change of phase of the underlying Markov process. We further allow for dependence between the different price dynamics. In this general regime-switching framework, we provide lower and upper bounds to the exact option prices based upon ideas from the literature without regime switching. These bounds are obtained via univariate Fourier inversion under the assumption that the joint characteristic functions of the Markov-modulated Lévy processes are known. We study these obtained spread and basket option price approximations in different regime-switching models. Several numerical experiments are included and these show that, especially, the lower bounds have a very high precision.

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Closed form spread option valuation

Cited by 58 publications

References 7 publications

Real option approach to evaluate cores for remanufacturing in service markets

Real option approach to evaluate cores for remanufacturing in service markets

Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options

Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

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