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Hedging with transient price impact for non-covered and covered options. (arXiv:1807.05917v1 [q-fin.PR])
来源于:arXiv
We solve the superhedging problem for European options in a market with
finite liquidity where trading has transient impact on prices, and possibly a
permanent one in addition. Impact is multiplicative to ensure positive asset
prices. Hedges and option prices depend on the physical and cash delivery
specifications of the option settlement. For non-covered options, where impact
at the inception and maturity dates matters, we characterize the superhedging
price as a viscosity solution of a degenerate semilinear pde that can have
gradient constraints. The non-linearity of the pde is governed by the transient
nature of impact through a resilience function. For covered options, the
pricing pde involves gamma constraints but is not affected by transience of
impact. We use stochastic target techniques and geometric dynamic programming
in reduced coordinates. 查看全文>>