Abstract: The so-called classical approach uses the first arbitrage relation and tries to extract a risk-adjusted model for the spot rate rt. This will involve modeling the drift of the spot rate dynamics, as well as calibration to observed volatilities. An assumption on the Markovness of rt is used along the way. The Heath–Jarrow–Morton (HJM) approach, on the other hand, uses the second arbitrage condition and obtains arbitrage-free dynamics of k dimensional instantaneous forward rates F(t,T). It involves no drift modeling, but volatilities need to be calibrated. It is more general, and, usually, less practical to use in practice. The HJM approach does not need spot-rate modeling. Yet, it also demonstrates that the spot rate rt is in general not Markov.In this chapter we provide a discussion of these methods used by practitioners in pricing interest-sensitive securities. Given our limited scope, numerical issues and details of the pricing computations will be omitted. Interested readers can consult several excellent texts on these. Our focus is on the understanding of these two fundamentally different approaches.
Publication Year: 2014
Publication Date: 2014-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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