PCP with dividend – intuitively

See also posts on PCP.
See also post on replicating fwd contract.

I feel PCP is the most intuitive, fundamental and useful “rule of thumb” in option pricing. Dividend makes things a tiny bit less straightforward.

C, P := call and put prices today
F := forward contract price today, on the same strike. Note this is NOT the fwd price of the stock.

We assume bid/ask spread is 0.

    C = P + F

The above formula isn’t affected by dividend — see the very first question of our final exam. It depends only on replication and arbitrage. Replication is based on portfolio of traded securities. (Temperature – non-tradable.) But a dividend-paying stock is technically non-tradable!

* One strategy – replicate with European call, European put and fwd contract. All tradable.

* One strategy – replicate with European call, European put, bond and dividend-paying stock, but no fwd contract. Using reinvestment and adjusting the initial number of shares, replication can still work. No need to worry about the notion that the stock is “non-tradable”.

Hockey stick, i.e. range-of-possibility graphs of expiration scenarios? Not very simple.

What if I must express F in terms of S and K*exp(-rT)? (where S := stock price any time before maturity.)

  F = S – D – K*exp(-rT) … where D := present value of the dividend stream.

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