论文标题
对风险中立概率的凸优化
Convex Optimization Over Risk-Neutral Probabilities
论文作者
论文摘要
我们考虑一系列取决于到期或到期时基础资产价格的衍生品。缺乏套利等同于价格上存在风险中立的概率分布。特别是，任何风险中性分布都可以解释为确定不存在套利的证书。我们对有多种风险中立概率的情况感兴趣。我们描述了一组风险中性价格概率集中的许多凸优化问题。这些包括计算累积分布，VAR，CVAR和其他数量的界限。在离散基础价格之后，这些问题成为有限的尺寸凸面或Quasiconvex优化问题，因此是可进行的。我们使用真正的选项和期货定价数据为标准普尔500指数和比特币说明了我们的方法。
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in particular, any risk neutral distribution can be interpreted as a certificate establishing that no arbitrage exists. We are interested in the case when there are multiple risk-neutral probabilities. We describe a number of convex optimization problems over the convex set of risk neutral price probabilities. These include computation of bounds on the cumulative distribution, VaR, CVaR, and other quantities, over the set of risk-neutral probabilities. After discretizing the underlying price, these problems become finite dimensional convex or quasiconvex optimization problems, and therefore are tractable. We illustrate our approach using real options and futures pricing data for the S&P 500 index and Bitcoin.
