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on Computational Economics |
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Issue of 2005‒11‒05
three papers chosen by |
| By: | Christian Fries |
| Abstract: | In this paper we investigate the so called foresight bias that may appear in the Monte-Carlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same Monte-Carlo simulation as the exercise values. The standard approach to remove the foresight bias is to use two independent Monte-Carlo simulations: One simulation is used to estimate the exercise criteria (as a function of some state variable), the other is used to calculate the exercise price based on this exercise criteria. We shall call this the numerical removal of the foresight bias. In this paper we give an exact definition of the foresight bias in closed form and show how to apply an analytical correction for the foresight bias. Monte Carlo price for different levels of aggregation. Starting with a single Monte Carlo simulation with 2048000 paths we price the same option with two, four, eight, etc. smaller simulations and average the prices. Foresight bias becomes a strong effect when aggregating prices from many small (2000-5000 paths) simulations. Our corrections improve the prices even if a very small number of paths (200) is used. Our numerical results show that this analytical removal of the foresight bias gives similar results as the standard numerical removal of the foresight bias. The analytical correction allows for a simpler coding and faster pricing, compared to a numerical removal of the foresight bias. Our analysis may also be used as an indication of when to neglect the foresight bias removal altogether. While this is sometimes possible, neglecting foresight bias will break the possibility of parallelization of Monte-Carlo simulation and may be inadequate for Bermudan options with many exercise dates (for which the foresight bias may become a Bermudan option on the Monte-Carlo error) or for portfolios of Bermudan options (for which the foresight bias grows faster than the Monte-Carlo error). |
| Keywords: | Monte Carlo, Bermudan, Early Exercise, Regression, Least Square Approximation of Conditional Expectation, Longstaff-Schwartz, Perfect Foresight, Foresight Bias |
| JEL: | C15 G13 |
| Date: | 2005–11–03 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpfi:0511002&r=cmp |
| By: | Andrew Cohen |
| Abstract: | This note presents a simple algorithm for characterizing the set of pure strategy Nash equilibria in a broad class of entry games. The algorithm alleviates much of the computational burden associated with recently developed econometric techniques for estimating payoff functions inferred from entry games with multiple equlibria. |
| Date: | 2004 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2005-37&r=cmp |
| By: | Joseph I. Daniel (Department of Economics, University of Delaware); Munish Pahwa (MBNA, Newark, DE) |
| Abstract: | We calculate mutual-best-response route networks for profit maximizing airlines serving large US air-traffic-hub cities. A simulated annealing algorithm determines which of over ten thousand potential routes receive direct or hub-and-spoke service. DOT’s Origin and Destination Survey is used to calibrate airline revenue and cost functions. Simulated route structures, airfares, passenger flows, and market concentration levels closely approximate actual US networks comprising over seventy percent of domestic air travel. The results support several controversial positions regarding airline competition. Average airfares by route are consistent with price-taking behavior. Existing industry concentration levels can be justified by cost-reducing economies of scale and scope. Control of multiple airports by individual airlines currently has minimal effects on airfares or passenger flows. Socially optimal route structures would concentrate traffic at fewer and larger airports—but reduce costs only modestly. Airport pricing and capacity can significantly affect network traffic patterns. Investigation of strategic pricing is left for future research. |
| Keywords: | Hub-and-spoke airline networks, simulated annealing, commercial aviation, airline competition, airline mergers, airfares, airport congestion, and airport capacity. |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:dlw:wpaper:05-07&r=cmp |