Problem bank

Problem 201 of 333HardFinanceP201

Zero-coupon bond under Vasicek

  1. Under the risk-neutral measure the short rate follows Vasicek, drt=λ(θ−rt) dt+σ dWtdr_t = \lambda(\theta - r_t)\,dt + \sigma\,dW_t, with r0=1%r_0 = 1\%, θ=4%\theta = 4\%, λ=0.5\lambda = 0.5 and σ=2%\sigma = 2\%. Price a zero-coupon bond paying 1 at T=5T = 5, that is, compute P(0,T)=E[e−∫0Trt dt]P(0, T) = E\big[e^{-\int_0^T r_t\,dt}\big]. What is the five-year yield?