Worked Examples — Change of Measure in Derivatives Pricing

The change-of-measure machinery developed in this topic has three recurring applications in quantitative finance: bond pricing under short-rate models, equity derivatives under GBM, and currency (quanto) derivatives where one currency's drift is adjusted for correlation. This capstone consolidates the pipeline — Girsanov + risk-neutral pricing + martingale representation — on concrete instruments:

1. Vasicek zero-coupon bond — bond price as a $\mathbb{Q}$-conditional expectation, affine form recovered from the Feynman-Kac connection.
2. European call under GBM — the full chain from drift removal to $d_1$/$d_2$, with the BS PDE recovered as a byproduct.
3. Quanto forward — correlation adjustment from FX measure change; convexity correction for pricing in the wrong currency.

1. Example 1: Vasicek Zero-Coupon Bond
2. Example 2: European Call Under GBM (The Full Chain)
3. Example 3: Quanto Forward — Currency Adjustment