Function-approximation-based Perfect Control Variates for Pricing American Options

Bolia, Nomesh B.; Juneja, S.

doi:10.1109/wsc.2005.1574464

Cited by 11 publications

(17 citation statements)

References 8 publications

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“…]dt} which is the average time during the call that price p t will be higher than the strike K. Paying once and in advance O 0 (T,i 0 ,K) the user is assured that the instantaneous price of the call will never exceed K. 3 A software agent in the terminal is programmed to react to O 0 (T,i 0 ,K) accepting or refusing the option contract after comparing this value with a threshold in dcent predefined by the user.…”

Section: Service Price Formulationsmentioning

confidence: 99%

“…Following this methodology to obtain the final price of the service, all formulas require a closed form solution to calculate the necessary parameters. But finding a closed form for equation (3) and (9) is a hard challenge. Instead, it is possible to estimate those parameters by the use of a numerical method, but to do this a discrete form for above equation must be written.…”

Section: Discretization Of the Problemmentioning

confidence: 99%

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An Innovative Pricing Method for Telecommunication Services Pricing through American Options

D'Acquisto

Cassarà

Alcuri³

2009

JNW

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With the evolution of telecommunication networks and of their services the role of service provider is changed, so nowadays there is a coexistence of Network Operators and Virtual Operators. The difference between these players is not in the way they offer a service but primarily in their economic objectives and risk attitudes. Essentially, Network Operators own their infrastructures and typically have to sustain both fixed costs (CAPEX) and recurrent costs (OPEX), while Virtual Operators may have a simpler cost structure, mainly consisting of OPEX for the hire of network resources. Since these two operators can provide the same service in two different markets, their objectives differ substantially: on one hand, Network Operators aim to recover their costs with traditional pricing schemes (flat or time based), while the goal of Virtual Operators is to stay in the market, trying to attract as more users as they can through innovative pricing schemes (time varying, congestion pricing) providing, at the same time, QoS levels comparable to the corresponding ones of Network Operators. From above considerations we can understand the importance for Virtual Operators and for Regulatory Agencies to develop new pricing schemes. To develop a new pricing scheme it is necessary to study a model that shows vs. time the occupancy of network resources and moreover we present a method to estimate the final price of the service offered from Virtual Operator, for a given occupancy state of network resources, which is evaluated by American Options Pricing Scheme. This manner it is possible to address the problems of co-existence in the same communication market of these two service providers and the one of prevention of possible arbitrage, driven by different pricing schemes.

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Section: Service Price Formulationsmentioning

confidence: 99%

Section: Discretization Of the Problemmentioning

confidence: 99%

An Innovative Pricing Method for Telecommunication Services Pricing through American Options

D'Acquisto

Cassarà

Alcuri³

2009

JNW

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“…Finally we conclude in Section 7 where we also discuss how our methodology specializes to some popular models. Significant portions of the analysis in this paper appeared in Bolia, Glasserman and Juneja (2004) and Bolia and Juneja (2005).…”

Section: Introductionmentioning

confidence: 99%

Variance reduction techniques for pricing American options using function approximations

Juneja¹,

Kalra²

2009

JCF

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simulation techniques that use function approximations have been successfully applied to approximately price multi-dimensional American options. However, for many pricing problems the time required to get accurate estimates can still be prohibitive and this motivates the development of variance reduction techniques. In this paper, we describe a zero-variance or 'perfect' control variate and a zero variance or 'perfect' importance sampling distribution to price American options. We also observe the natural connection of the perfect control variate to additive duality and the perfect importance sampling distribution to multiplicative duality in American options. We then discuss how function approximations may be used to approximate the perfect control variate and the perfect importance sampling distribution. Empirically, we observe that both the techniques give significant variance reduction on examples of single and multi-dimension options.

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“…For the applications we have in mind this assumption is unlikely to hold. Bolia and Juneja [2005] use the martingale control variates developed in Henderson and Glynn [2002], as we do, but in the case of linearly parameterized controls. Maire [2003] expresses the estimation problem as an integration problem over the unit hypercube, and uses the expansion of the integrand for an approximate orthonormal basis as a control variate.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Control Variates for Finite-Horizon Simulation

Kim

Henderson

2007

Mathematics of OR

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Adaptive Monte Carlo methods are simulation efficiency improvement techniques designed to adaptively tune simulation estimators. Most of the work on adaptive Monte Carlo methods has been devoted to adaptively tuning importance sampling schemes. We instead focus on adaptive methods based on control variate schemes. We introduce two adaptive control variate methods, and develop their asymptotic properties. The first method uses stochastic approximation to adaptively tune control variate estimators. It is easy to implement, but it requires some non-trivial tuning of parameters. The second method is based on sample average approximation. Tuning is no longer required, but it can be computationally expensive. Numerical results for the pricing of barrier options are presented to demonstrate the methods.

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Function-approximation-based Perfect Control Variates for Pricing American Options

Cited by 11 publications

References 8 publications

An Innovative Pricing Method for Telecommunication Services Pricing through American Options

An Innovative Pricing Method for Telecommunication Services Pricing through American Options

Variance reduction techniques for pricing American options using function approximations

Adaptive Control Variates for Finite-Horizon Simulation

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