Discounting and Present Value
A CHF tomorrow is worth less than a CHF today. Discounting converts future cash flows to today.
Discounting uses an interest rate curve: PV = Σ cashflow_t × DF(t).
In no-arbitrage pricing, discount factors come from tradable instruments (or a model tied to them).
Mis-specified discounting shifts valuations systematically.
A fixed stream of future cash flows can be viewed in two ways: their nominal amounts at payment dates, and their discounted contributions to present value at time 0. The discount rate compresses or stretches these contributions along the timeline.
Increasing the discount rate shrinks the green bars more strongly at later times: far cash flows count less in today’s value. The present value is the sum of these discounted contributions, not the sum of nominal amounts.
In practice, each maturity has its own discount factor from the rate curve; here we use a single flat r for clarity. Mis-calibrated discount factors move the whole term structure of PVs.