大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Price Discrepancy and Optimal Timing to Buy Derivatives

Tim Leung (Johns Hopkins University)

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大証寄附研究部門セミナーシリーズ 第24回

Price Discrepancy and Optimal Timing to Buy Derivatives

Tim Leung (Johns Hopkins University)

In incomplete markets, where not all risks can be hedged, different risk-neutral or risk-averse pricing models may yield a range of no-arbitrage prices. Consequently, the investor's model price may disagree with the market price. This leads to the natural and important question of when is the optimal time to buy a derivative security from the market.

We consider an investor who attempts to maximize the spread between her model price and the offered market price through optimally timing the purchase. Both the investor and the market value the options by risk-neutral expectations but under different equivalent martingale measures representing different market views or risk premia specifications. We show that the structure of the resulting optimal stopping problem depends on the interaction between the respective market price of risk and the option payoff. In particular, a crucial role is played by the delayed purchase premium that is related to the stochastic bracket between the market price and the buyer's risk premia. Explicit characterization of the purchase timing and numerical examples are given for two representative classes of Markovian models: (i) defaultable equity models with local intensity; (ii) diffusion stochastic volatility models.