Applying Bayesian Inference to Freight Rate Models
In real-world freight markets, we deal with more complex scenarios. Let’s consider two popular
models: a simple mean-reverting model and a more sophisticated stochastic volatility model.
MEAN-REVERTING FREIGHT RATE MODEL Shipping markets are known for their mean- reverting characteristics
1. In periods of high rates, increased vessel supply tends to bring rates down, while in periods of low rates, reduced supply or increased demand can push rates up. A simple mean-reverting model for freight rates can be expressed as:
STOCHASTIC VOLATILITY MODEL FOR FREIGHT RATES A more sophisticated model might incorporate stochastic volatility, similar to the Heston model in financial markets:
1. For the freight rate:
2. For the volatility:
Where: rt is the freight rate at time t κ is the speed of mean reversion θ is the long-term mean freight rate σ is the volatility of freight rates Wt is a Wiener process
Where: vt is the stochastic volatility α is the rate of mean reversion for volatility β is the long-term mean of volatility ξ is the volatility of volatility Wt1 and Wt2 are correlated Wiener processes
Bayesian Inference in Action: Updating Freight Market Beliefs When applying Bayesian inference to these models, we start with prior beliefs
about the parameters (like $\kappa$ in the mean-reverting model) and update these beliefs as we observe market data.
Initial Prior We begin with an initial guess about the
distribution of $\kappa$. If we’re unsure, we might use a flat distribution (Jeffreys prior)
Updating Beliefs
As we observe freight rate movements, we repeatedly apply
Bayesian inference to update our
distribution of $\kappa$. Convergence Over time, our beliefs
about $\kappa$ should converge towards its
true value, reflecting the actual mean reversion speed in the market.
12 | ADMISI - The Ghost In The Machine | Q1 Edition 2025
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