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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.07154 |
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| _version_ | 1866915810653503488 |
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| author | Tiwari, Priyanshu Majumdar, Sourav |
| author_facet | Tiwari, Priyanshu Majumdar, Sourav |
| contents | We develop a tractable framework for valuing Asian options when trading the underlying generates market impact and execution costs. Starting from a discrete-time, quote-level model, we construct a reference midpoint suitable for Asian payoffs and separate market impact into a transient component and a permanent drift distortion driven by signed trading. This specification admits continuous-time limits where the midpoint and impact state converge to a coupled system in which the midpoint drift depends on the transient impact state and in the endogenous regime on the hedger's trading rate, with correlated price and order-flow shocks.
We study valuation in two complementary regimes. In an exogenous benchmark, the impact state evolves independently of the hedger. When the order-flow volatility is deterministic, we obtain a closed-form expression for the geometric Asian call. In an endogenous regime, trading volumes feed back into prices and costs, leading to a stochastic control problem and Hamilton-Jacobi-Bellman equations. We define reservation bid and ask prices via cost-based indifference which produces an impact-driven bid-ask spread. For computations, we propose a CRR-style tree-based Bellman algorithm. Numerical experiments show that exogenous impact effects are modest relative to frictionless benchmarks, while endogenous indifference prices generate nontrivial bid-ask spreads that grow super-linearly in impact parameters, widen when execution costs are lower, and shrink with faster mean reversion, highlighting the interaction between averaging in Asian options, price impact effects, and strategic trading. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asian option valuation under price impact Tiwari, Priyanshu Majumdar, Sourav Mathematical Finance We develop a tractable framework for valuing Asian options when trading the underlying generates market impact and execution costs. Starting from a discrete-time, quote-level model, we construct a reference midpoint suitable for Asian payoffs and separate market impact into a transient component and a permanent drift distortion driven by signed trading. This specification admits continuous-time limits where the midpoint and impact state converge to a coupled system in which the midpoint drift depends on the transient impact state and in the endogenous regime on the hedger's trading rate, with correlated price and order-flow shocks. We study valuation in two complementary regimes. In an exogenous benchmark, the impact state evolves independently of the hedger. When the order-flow volatility is deterministic, we obtain a closed-form expression for the geometric Asian call. In an endogenous regime, trading volumes feed back into prices and costs, leading to a stochastic control problem and Hamilton-Jacobi-Bellman equations. We define reservation bid and ask prices via cost-based indifference which produces an impact-driven bid-ask spread. For computations, we propose a CRR-style tree-based Bellman algorithm. Numerical experiments show that exogenous impact effects are modest relative to frictionless benchmarks, while endogenous indifference prices generate nontrivial bid-ask spreads that grow super-linearly in impact parameters, widen when execution costs are lower, and shrink with faster mean reversion, highlighting the interaction between averaging in Asian options, price impact effects, and strategic trading. |
| title | Asian option valuation under price impact |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2512.07154 |