Free module · Options & volatility
Options: Payoffs, Replication & Hedge Accounting
Understand nonlinear contracts before trusting a pricing or hedging model.
calls · puts · spreads · parity · binomial replication · Greeks · exercise
The building blocks
An option exchanges an upfront premium for a conditional future payoff. Payoff, present value and net profit are different quantities.
- Write the exact contract and terminal cash flows.
- Replicate simple states and price under explicit assumptions.
- Hedge and reconcile costs across a path.
Lessons in this module
- 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
Practice and apply
- Call payoff is not profit — European call, strike 100, expiry price 108, premium 5, multiplier 100; no financing or fees.
- Match two payoff states — Stock now 100, next prices 120/80; call pays 20/0; cash gross return 1.
- Reconcile one hedge interval — Short one call rises 5 to 6.1; long .5 share rises 100 to 102; total costs .05.
Work through the practice exercises · Quant development tools