The Optimal Hedging Ratio for Contingent Claims Based on Different Risk Aversions

This paper estimates optimal hedging ratios for a Finnish spring wheat producer under price and yield uncertainty. The contract available for hedging fixes the price and quantity at the time of sowing for a delivery at harvest. Autoregressive models are used to obtain point forecasts for the conditional mean price and price volatility at harvest. Expected yield and yield volatility are estimated from the field experiment data. A range of coefficients of absolute risk aversion are used in the computations. The results suggest that yield volatility is large and it dominates the price volatility in the optimal hedging decisions of the Finnish wheat producers. The point estimate for the price and yield correlation is negative and has a large magnitude. Thus, a negative correlation between the price and the yield, as signalled by the point estimate, will decrease the optimal hedging ratio since the Finnish farmers do not have access to selling put options when they enter in a forward contract.;

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LOCALLY RISK-MINIMIZING HEDGING FOR EUROPEAN CONTINGENT CLAIMS WRITTEN ON NON-TRADABLE ASSETS WITH COMMON JUMP RISK

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964820000686 ◽

2021 ◽

pp. 1-25

Author(s):

Xiaonan Su ◽

Yu Xing ◽

Wei Wang ◽

Wensheng Wang

Keyword(s):

Closed Form Solution ◽

Contingent Claims ◽

Form Solution ◽

Martingale Measure ◽

Call Option ◽

Transform Method ◽

Jump Risk ◽

European Call Option ◽

Hedging Strategies ◽

Optimal Hedging

This article investigates the optimal hedging problem of the European contingent claims written on non-tradable assets. We assume that the risky assets satisfy jump diffusion models with a common jump process which reflects the correlated jump risk. The non-tradable asset and jump risk lead to an incomplete financial market. Hence, the cross-hedging method will be used to reduce the potential risk of the contingent claims seller. First, we obtain an explicit closed-form solution for the locally risk-minimizing hedging strategies of the European contingent claims by using the Föllmer–Schweizer decomposition. Then, we consider the hedging for a European call option as a special case. The value of the European call option under the minimal martingale measure is derived by the Fourier transform method. Next, some semi-closed solution formulae of the locally risk-minimizing hedging strategies for the European call option are obtained. Finally, some numerical examples are provided to illustrate the sensitivities of the optimal hedging strategies. By comparing the optimal hedging strategies when the underlying asset is a non-tradable asset or a tradable asset, we find that the liquidity risk has a significant impact on the optimal hedging strategies.

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