In this article, we define a hedging strategy in a setting typical for the commodity market. Firstly, we prove the existence of the locally risk-minimizing (LRM) hedging strategy for payment streams in this setting. Next, a three-step procedure is described to determine the LRM hedging strategy. Then the procedure is illustrated for stochastic volatility models, as these models are a special case of the non-traded situation which frequently occurs in the commodity markets. Finally, we introduce the (adjusted) LRM hedging strategy in the non-traded setting and for this specific setting we numerically show the outperformance of this strategy compared with current market practices
The theory of conic finance replaces the classical one-price model by a two-price model by determining bid and ask prices for future terminal cash flows in a consistent manner. In this framework, we derive closedform solutions for bid and ask prices of plain vanilla European options, when the density of the log-returns is log-concave. Assuming that log-returns are normally or Laplace distributed, we apply the results to a time-series of real market data and compute an implied liquidity risk premium to describe the bid-ask spread. We compare this approach to the classical attempt of describing the spread by quoting Black-Scholes implied bid and ask volatilities and demonstrate that the new approach characterize liquidity over time significantly better.
In this paper, a multivariate constrained robust M‐regression method is developed to estimate shaping coefficients for electricity forward prices. An important benefit of the new method is that model arbitrage can be ruled out at an elementary level, as all shaping coefficients are treated simultaneously. Moreover, the new method is robust to outliers, such that the provided results are stable and not sensitive to isolated sparks or dips in the market. An efficient algorithm is presented to estimate all shaping coefficients at a low computational cost. To illustrate its good performance, the method is applied to German electricity prices.
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