An Actuarial Layman's Guide to Building Stochastic Interest Rate Generators
نویسنده
چکیده
A stochastic interest rate generator is a valuable actuarial tool. The parameters that specify a stochastic model of interest rates can be adjusted to make the model arbitrage-free, or they can be adjusted to accommodate an individual investor's subjective views. The arbitrage-free settings of the parameters must be used when pricing streams of interest-rate-contingent cash flows, for example, when establishing the risk-neutral position for assetliability management. The real-world settings of the parameters should be used when evaluating the risk-reward tradeoffs inherent in deviating from the risk-neutral position. Without relying on formulas, this paper presents the important concepts underlying the theory of arbitrage-free pricing of interest-rate-contingent cash flows: absence of opportunities for riskless arbitrage; completeness of markets; relative prices that do not depend on individual investors' subjective views or risk preferences; and expected-value pricing in the risk-neutral world. Using these concepts, the paper then describes the steps required to build continuous stochastic models of interest rates, including models that are either partially or fully arbitrage free. After studying the paper, all actuaries should be able to comprehend better some of the literature in this important subject area. Then, after studying some of the technical references, many actuaries should be in a position to begin to build their own practical models.
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