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Cash accounting for a discretely hedged option
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Start with the idea
A hedge outcome is the combined option and underlying cash flow, after all costs and financing.
Symbols, units & horizon
- n: signed option units covering one underlying unit each
- V₀,V₁: option values per unit at interval endpoints
- h: signed underlying units held fixed during interval
- S₀,S₁: underlying prices per unit
- c: total interval costs in currency, including any chosen financing charge
- Π: interval marked profit in currency
When and why to use this
Reconcile hedge P&L and distinguish model error from trading and financing costs.
A hedge outcome is the combined option and underlying cash flow, after all costs and financing.
For one interval with a fixed stock hedge, record the change in option value and stock value using signed quantities. A short call hedged by long stock has opposite option and stock contributions. Match entry and exit timestamps and valuation conventions.
A multi-period hedge needs a self-financing cash ledger for every rebalance, accrued cash interest, dividends and transaction fees. This one-interval calculation is a building block, not a complete dynamic hedge simulator.
Cash accounting for a discretely hedged option
- Multiply option price change by signed option quantity.
- Multiply underlying price change by held hedge quantity.
- Add both contributions and subtract the explicitly itemized costs.
Short one call rises from 5 to 6.1; hold .5 share rising from 100 to 102; costs .05. Profit=−1.1+1−.05=−.15.
Apply it in a strategy
- Freeze inputs at the stated decision time and record their units.
- Reconcile hedge P&L and distinguish model error from trading and financing costs.
- Recompute the example, then change the material assumption and explain the difference.
Research deliverable
Cash accounting for a discretely hedged option: produce the worked calculation, a timestamped input record and a written decision addressing this limitation: Mixing theoretical option marks with executable hedge prices can distort comparisons.
These are synthetic mechanics examples, not historical performance or paper replications. Module evidence and research boundaries record the 12 September 2026 review.
Python implementation
Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.
# Python 3.10+; standard library and NumPy only.
# Synthetic teaching inputs; conventions and units are defined in the notation above.
def hedge_interval(option_units,option_before,option_after,shares,spot_before,spot_after,cost):
if cost<0: raise ValueError('Nonnegative cost required')
return option_units*(option_after-option_before)+shares*(spot_after-spot_before)-cost
assert abs(hedge_interval(-1,5,6.1,.5,100,102,.05)+.15)<1e-12
print(hedge_interval(-1,5,6.1,.5,100,102,.05))Continue learning
Options: Payoffs, Replication & Hedge Accounting — all lessons- Call and put payoffs versus profit
- A bull call spread caps gains and initial cost
- Put–call parity as identical terminal cash flows
- Replicate a one-step option with stock and cash
- Black–Scholes as a conditional benchmark
- Delta and gamma are local sensitivities
- Cash accounting for a discretely hedged option
- Early exercise compares immediate and continuation value
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