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2

With only a short rate $r_t$ (not a tradable asset) given, we have a context where there is no risky asset, but there is at least one Brownian motion driver (incomplete market model). The only traded asset is the bank account given by: $$ d\beta_t = r_t \beta_t dt, \; \beta_0 = 1, $$ which is a locally riskless asset. Zero-coupon bonds would be viewed as ...


4

I recommend two papers that should help you with this exercise. The first is "Kalman Filtering of Generalized Vasicek Term Structure Models." This paper provides a general framework for calibrating term structure models using the Kalman filtering technique. The method is capable of disentangling the parameters under the risk neutral and physical ...


3

A famous (APT) factor pricing model was developed by Chen, Ross and Roll (1986). The model suggests $$R_{i,t}=a_i + \beta_{i,MP}MP_t + \beta_{i,UI}UI_t + \beta_{i,DEI}DEI_t+\beta_{i,UPR}UPR_t+\beta_{i,UTS}UTS_t+\varepsilon_{i,t},$$ where $\varepsilon_{i,t}$ is an idiosyncratic term. The factors are not all tradable returns. $UPR$ and $UTS$ are, but $MP$, $UI$...


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