研究期間：10108~10207;The state price density (SPD) is the density function under the equivalent martingale for derivative pricing and is also known as the risk-neutral density. SPD is usually calibrated from frequently traded options and can be used to price illiquid options and risk management. Recently, SPD is used for developing profitable statistical arbitrage trading strategies, and is used for investigating investors' risk aversion functions. Joint SPD is the joint state price density for options with multiple underlying assets (also known as rainbow options), and has been of critical importance along with the rapid development of more complicated financial innovations in practice. However, to the best of our knowledge, little has been known about how to calibrate the joint SPD from rainbow options properly. This research proposal aims at proposing a general account of joint SPD estimation. We start with Black-Scholes assumptions. However, to relax the Gaussian dependence structure, we consider a joint SPD modeling via a copula framework, where marginal distributions are assumed to be a from some common parametric distributions and are linked via a suitable copula. We further generalize such a parametric setting to semi- and nonparametric counterparts to avoid model misspecification. Furthermore, because the calculation of model prices calculating, our second aim is to proposing variance reduction techniques for rainbow option pricing. For example, an importance sampling method using an exponentially tilted formula is employed to minimize the variance of the importance sampling estimators.
