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Fixed Income and Interest-Rate Models / No-Arbitrage Pricing and the Risk-Neutral Framework

Derivation — Radon-Nikodym Density and Bond Option Pricing

This is a derivation sub-note for Change of Numeraire and the T-Forward Measure. It carries the algebra of the Margrabe decomposition through to a closed-form bond option price under Gaussian bond dynamics. No new concepts are introduced here — only the detailed computation that was deferred in the parent lesson.

In this lesson

    1. Setup: Gaussian bond dynamics under Q\mathbb{Q}
    1. The Radon-Nikodym density between forward measures
    1. Computing the two forward-measure probabilities
    1. The closed-form bond option price
    1. Vasicek model — computing VPV_P
    1. European put and put-call parity

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