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Computational Methods in Finance is developed from the author's courses at Columbia University and the Courant Institute of New York University. This text is designed for graduate students in financial engineering and mathematical finance as well as practitioners. It will help readers accurately price a vast array of derivatives.

Rational expectations (Economic theory)

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Central banks in major industrialized economies were slow to react to the surge in inflation that began in early 2021. The proximate causes of this surge were the supply chain disruptions associated with the easing of COVID restrictions, fiscal policies designed to cushion the economic impact of COVID, and the impact on commodity prices and supply chains of the war in Ukraine. We investigate the consequences of policy delay in responding to inflation shocks. First, using a simple three-period model, we show how policy delay worsens inflation outcomes, but can mitigate or even reverse the output decline that occurs when policy responds without delay. Then, using a calibrated new Keynesian framework and two measures of loss that incorporate a “balanced approach” to weigh inflation and the output gap, we find that loss is monotonically increasing in the length of the delay. Loss is reduced if policy, when it does react, is more aggressive. To investigate whether these results are sensitive to the assumption of rational expectations, we consider cognitive discounting as an alternative assumption about expectations. With cognitive discounting, forward guidance is less powerful and results in a reduction in the costs of delay. Under either assumption about expectations, the costs of a short delay can be eliminated by adopting a less inertial policy rule and a more aggressive response to inflation.

Banking --- Banks and Banking --- Central bank policy rate --- Central Banks and Their Policies --- Credit --- Currency crises --- Deflation --- Economic & financial crises & disasters --- Economic theory & philosophy --- Economic Theory --- Economic theory --- Economics of specific sectors --- Economics --- Economics: General --- Expectations --- Finance --- Financial services --- Inflation --- Informal sector --- Interest rates --- Interest Rates: Determination, Term Structure, and Effects --- Macroeconomics --- Macroeconomics: Production --- Monetary Policy --- Money Multipliers --- Money Supply --- Output gap --- Policy Coordination --- Policy Designs and Consistency --- Policy Objectives --- Price Level --- Prices --- Production and Operations Management --- Production --- Rational expectations --- Real interest rates --- Speculations