Abstract
We consider rate swaps which pay a fixed rate against a floating rate in
presence of bid-ask spread costs. Even for simple models of bid-ask spread
costs, there is no explicit strategy optimizing an expected function of the
hedging error. We here propose an efficient algorithm based on the stochastic
gradient method to compute an approximate optimal strategy without solving a
stochastic control problem. We validate our algorithm by numerical experiments.
We also develop several variants of the algorithm and discuss their
performances in terms of the numerical parameters and the liquidity cost.
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