Vasicek (1977) Posits a General Mean-Reverting Form for the Short-Rate $d r _ { t } = \kappa \left( \theta - r _ { t } \right) d t + \sigma d W _ { t }$

question 15

Multiple Choice

Vasicek (1977) posits a general mean-reverting form for the short-rate: $d r _ { t } = \kappa \left( \theta - r _ { t } \right) d t + \sigma d W _ { t }$ He then derives, in the absence of arbitrage, a restriction on the market price of risk $\lambda$ of any bond, where $( \mu - r ) / \eta = \lambda$ of any bond, with $\mu$ being the instantaneous return on the bond, and $\eta$ being the bond's instantaneous volatility. The derived restriction is that

• A) \(\lambda\) is a constant.
• B) \(\lambda\) may be a function of time \(t\) , but not of any other time- \(t\) information or of the maturity \(T\) of the bond.
• C) \(\lambda\) may be a function of the time- \(t\) short rate \(r _ { t }\) , but not of current time \(t\) or of the bond maturity \(T\) .
• D) \(\lambda\) may be a function of time \(t\) and the time- \(t\) short rate \(r _ { t }\) , but not of the bond maturity \(T\) .

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