Working Paper: CEPR ID: DP8402
Authors: Suleyman Basak; Georgy Chabakauri
Abstract: Despite much work on hedging in incomplete markets, the literature still lacks tractable dynamic hedges in plausible environments. In this article, we provide a simple solution to this problem in a general incomplete-market economy in which a hedger, guided by the traditional minimum-variance criterion, aims at reducing the risk of a non-tradable asset or a contingent claim. We derive fully analytical optimal hedges and demonstrate that they can easily be computed in various stochastic environments. Our dynamic hedges preserve the simple structure of complete-market perfect hedges and are in terms of generalized "Greeks," familiar in risk management applications, as well as retaining the intuitive features of their static counterparts. We obtain our time-consistent hedges by dynamic programming, while the extant literature characterizes either static or myopic hedges, or dynamic ones that minimize the variance criterion at an initial date and from which the hedger may deviate unless she can pre-commit to follow them. We apply our results to the discrete hedging problem of derivatives when trading occurs infrequently. We determine the corresponding optimal hedge and replicating portfolio value, and show that they have structure similar to their complete-market counterparts and reduce to generalized Black-Scholes expressions when specialized to the Black-Scholes setting. We also generalize our results to richer settings to study dynamic hedging with Poisson jumps, stochastic correlation and portfolio management with benchmarking.
Keywords: Benchmarking; Correlation; Risk; Derivatives; Discrete Hedging; Hedging; Incomplete Markets; Minimum-Variance Criterion; Poisson Jumps; Risk Management; Time-Consistency
JEL Codes: C61; D81; G11
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Dynamic hedges (C69) | Reduction in hedging error variance (C51) |
| Hedging strategy (G13) | Quality of risk management outcomes (L15) |
| Higher volatility of non-tradable asset (G19) | Decrease in hedging effectiveness (G19) |
| Stochastic processes (C69) | Efficacy of hedging strategy (G13) |
| Market incompleteness (D52) | Hedging policy (G52) |