关于永生生物的入门
A primer on perpetuals
摘要：
我们考虑一个无套利和无交易费用的连续时间金融市场。在这种情况下，我们引入了两种类型的永续合约，其中一种是长期方的收益是基础投资者的固定函数，长期方向短期方支付资金利率，另一种是长期方的收益是基础投资者的固定函数乘以随时间变化的贴现因子，但不需要支付资金。假设资产价格连续且严格为正，我们推导出无模型表达式的资金利率和贴现率的这些永久合同，以及复制策略的短边。当资产价格可以跳，我们得到的资金和贴现率，这是半稳健的意义上说，他们不依赖于动态的波动过程中的基础风险资产，但取决于市场的定价措施下的跳跃强度的表达式。当资产价格可以跳跃，波动过程是独立的基础风险资产，我们得到了一个明确的复制策略的长期合同的短边。在整个文件中，我们通过例子来说明具体的永久合同如何与传统的金融工具，如方差互换和杠杆交易所交易基金。
英文摘要：
We consider a continuous-time financial market with no arbitrage and no transactions costs. In this setting, we introduce two types of perpetual contracts, one in which the payoff to the long side is a fixed function of the underlyers and the long side pays a funding rate to the short side, the other in which the payoff to the long side is a fixed function of the underlyers times a discount factor that changes over time but no funding payments are required. Assuming asset prices are continuous and strictly positive, we derive model-free expressions for the funding rate and discount rate of these perpetual contracts as well as replication strategies for the short side. When asset prices can jump, we derive expressions for the funding and discount rates, which are semi-robust in the sense that they do not depend on the dynamics of the volatility process of the underlying risky assets, but do depend on the intensity of jumps under the market's pricing measure. When asset prices can jump and the volatility process is independent of the underlying risky assets, we derive an explicit replication strategy for the short side of a perpetual contract. Throughout the paper, we illustrate through examples how specific perpetual contracts relate to traditional financial instruments such as variance swaps and leveraged exchange traded funds.
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