Heterogeneous Ambiguity and Intermediary Asset Pricing


hanjyu - Posted on 16 November 2017

Project Description: 

Theoretical model in macro-finance.

Research Project Details
Project Duration: 
05/2017 to 09/2019
Project Significance: 
We model the dynamics of asset prices in general equilibrium with intermediary sector in segmented markets where households (infra-marginal investor) and specialists (marginal investor) have heterogeneous ambiguity. The model produces mechanisms of how heterogeneous ambiguity transmits into asset market and generates amplification effect both in and out of financial crisis. The heterogeneity can never be aggregated away in equilibrium since both ambiguities will induce low total risk exposure and asset price, as well as high risk premium and Sharpe ratio, with the latter dominated by marginal investor's ambiguity under constraint. During financial crisis, two ambiguities are endogenous in effective financial constraint as a scaled ratio thus accelerate the tightness of equity capital constraint in opposite direction. Higher household ambiguity lowers risky asset portfolio share by i) increasing wealth contribution into intermediation due to demand for expertise and ii) matching higher total equity capital with lower risky asset price in general equilibrium. On the contrary, a rise in marginal investor's ambiguity will increase the risky asset portfolio holding because of i) losing household equity capital by losing expertise and ii) lower asset price and higher return trigger a higher portfolio demand for risky asset. Under observational equivalence with homogeneous effective risk aversion and lower specialist ambiguity, the heterogeneity aggregates out through effective financial constraint. During non-crisis, higher specialist ambiguity lowers the risk exposure contract share and risky asset volatility. Moreover, asset price dynamics with heterogeneous ambiguity are endogenously determined in closed forms as functions of specialist's wealth. We solve the wealth process in general equilibrium which is highly non-linear but non-degenerate in steady state after considering ambiguity. The wealth distribution is stationary and fat-tailed by simulation. We also show non-unit elasticity of substitution in recursive utility only changes goods market but not effective financial constraint thus won't change the major asset price dynamics.
Remarks: 
In order to simulate the heterogeneity in parameters, we need to discretise the parameter into 20 values matrix. Moreover, in However, in order to generate the stationary wealth distribution (state variable), we need the time length at least 1e6(year)*12(monthly). Further, to let the sample doesn't depend on the initial value, we need the sample path to be more than 1e4. Then this created a huge matrix for the state variables and need a large storage for the computer. Lastly, we need to use this state variable matrix to generate the dynamics of more than 20 control variables. This further requires a large storage. So I would like to ask for a gridpoint to facilitate my simulation.
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