Optimal Volatility Dependent Derivatives in the Stochastic Volatility Model

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.