Optimal Volatility Dependent Derivatives in the Stochastic Volatility Model

Artem Dyachenko,Marc Oliver Rieger
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Abstract

We consider derivatives that maximize an investor’s expected utility in the stochastic volatility model. We show that the optimal derivative that depends on the stock and its variance significantly outperforms the optimal derivative that depends on the stock only. Such derivatives yield a much higher certainty equivalent return. This result implies that investors could benefit from structured financial products constructed along these ideas. TOPICS: Derivatives, fixed income and structured finance Key Findings ▪ A derivative is optimal if it maximizes an investor’s expected utility. In the stochastic volatility model, the optimal buy-and-hold derivative with the payoff that depends on the stock price and its volatility incorporates both the market risk premium and the variance risk premium. ▪ The optimal buy-and-hold derivative with the payoff that depends on the stock price and its volatility usually outperforms significantly both the optimal buy-and-hold derivative with the payoff that depends on the stock price only and the optimal buy-and-hold portfolio made up of the stock and the risk-free bond. ▪ Investors could benefit from derivatives with payoffs that depend on the stock price and its volatility.
随机波动率模型中的最优波动率相关导数
我们考虑在随机波动模型中使投资者期望效用最大化的衍生品。我们表明,依赖于股票及其方差的最优导数明显优于仅依赖于股票的最优导数。这类衍生品产生的确定性等效回报要高得多。这一结果表明,投资者可以从按照这些理念构建的结构性金融产品中获益。主题:衍生工具,固定收益和结构性金融主要发现▪如果衍生工具能使投资者的预期效用最大化,那么它就是最优的。在随机波动率模型中,收益取决于股票价格及其波动率的最优买入持有衍生品同时包含市场风险溢价和方差风险溢价。▪收益取决于股票价格及其波动性的最佳买入并持有衍生工具,通常明显优于收益仅取决于股票价格的最佳买入并持有衍生工具,以及由股票和无风险债券组成的最佳买入并持有投资组合。▪投资者可以从衍生品中获益,衍生品的收益取决于股价及其波动性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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