Quantile hedging and minimizing the expected shortfall for bond options

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  • 債権オプションに対するクォンタイル・ヘッジおよび期待不足額の最小化

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Föllmer and Leukert ([2, 3]) investigated the quantile hedging problem and the shortfall risk hedging problem for options of stocks. In the first part of this paper, the quantile hedging problems for options of bonds and for caplets are formulated. We derive a formula of the success probability for Ho-Lee bond model with the market price of risk γ which is equal to σt + c where σ is the volatility and c is a constant. Furthermore a lower bound of the success probability is calculated for caplets with the market price of risk γ which is equal to σt + c. 　In the second part of this paper the shortfall risk problems for options of bonds and for caplets are formulated. We give a formula of the minimal expected shortfall for Ho-Lee bond model with the constant market price of risk.

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