CONTENTS

Solution: From Physical Drift to Risk-Neutral Drift

Exercise: From Physical Drift to Risk-Neutral Drift

Solution

Since dWtP=dWtQ−θdtdW_t^{\mathbb{P}}=dW_t^{\mathbb{Q}}-\theta dt,

dSt=μStdt+σSt(dWtQ−θdt)=(μ−σθ)Stdt+σStdWtQ.dS_t=\mu S_tdt+\sigma S_t(dW_t^{\mathbb{Q}}-\theta dt)=(\mu-\sigma\theta)S_tdt+\sigma S_tdW_t^{\mathbb{Q}}.

With θ=(μ−r)/σ\theta=(\mu-r)/\sigma, μ−σθ=r\mu-\sigma\theta=r.

Takeaways

  • Girsanov shifts Brownian drift.
  • Volatility is unchanged.
  • The market price of risk is θ=(μ−r)/σ\theta=(\mu-r)/\sigma in this one-factor model.
Sign in to track progress
Solution - From Physical Drift to Risk-Neutral Drift | q4quant.studio